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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find the nth term of the geometric sequence with the given values.10100 ,−1098 ,1096 , . . . ; n = 51
Find the nth term of the arithmetic sequence with the given values.a1 = b, a3 = 5b, n = 25
Find the sum of each sequence with the indicated values.a1 = −4, n = 15, a15 = 17 (arith.)
Expand and simplify the given expressions by use of Pascal’s triangle.(x − 4)5
Find the sums of the given infinite geometric series.(1 + √2) − 1 + (√2 − 1) − . . .
Find the nth term of the geometric sequence with the given values.−2, 4k,−8k2 , . . . ; n = 6
Find the nth term of the arithmetic sequence with the given values.a1 = −c, a4 = 8c, n = 30
Find the sum of each sequence with the indicated values.a1 = 300, d = −30/3, n = 10
Expand and simplify the given expressions by use of Pascal’s triangle.(2a + 1)6
Find the fractions equal to the given decimals.0.33333 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.1/8 + 1/2 + 2 . . . + 32
Find the sum of the n terms of the indicated arithmetic sequence.4 + 8 + 12 + . . . + 64
Find the sum of each sequence with the indicated values.a1 = 16, r = −1/3, n = 14
Expand and simplify the given expressions by use of Pascal’s triangle.(x − 3)7
Find the fractions equal to the given decimals.0.272727 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.162 − 54 + 18 − . . . −2/3
Find the sum of the n terms of the indicated arithmetic sequence.27 + 24 + 21 + . . . + (−9)
Find the sum of each sequence with the indicated values.a1 = 64, an = 729, n = 7 (geom., r > 0)
Find the first four terms of the indicated expansions.(x + 2)10
Find the fractions equal to the given decimals.0.499999 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.384, 192, 96, . . . , n = 7
Find the sum of the n terms of the indicated arithmetic sequence.−2,−5/2 ,−3, . . . ; n = 10
Find the indicated quantities for the appropriate sequences.a1 = 17, d = −2, n = 9, S9 = ?
Find the first four terms of the indicated expansions.(x − 4)8
Find the fractions equal to the given decimals.0.999999 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.a1 = 9, an = −243, n = 4
Find the sum of the n terms of the indicated arithmetic sequence.3k, 10/3k, 11/3k, . . . ; n = 40
Find the indicated quantities for the appropriate sequences.d = 4/3, a1 = −3, an = 17, n = ?
Find the first four terms of the indicated expansions.(2a − 1)7
Find the fractions equal to the given decimals.0.404040 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.a1 = 96, r = −k/2, n = 10
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence.5, 13, 21, . . . , 45
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence. a₁ = , n = 20, S20 = 40
Find the indicated quantities for the appropriate sequences.a1 = 4, r = √2, n = 7, a7 = ?
Find the first four terms of the indicated expansions.(3b + 2)9
Find the fractions equal to the given decimals.0.070707 . . .
Find the sum of the first n terms of the indicated geometric sequence with the given values.log 2, log 4, log 16, . . . ; n = 6
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence.−2,−1.5,−1, . . . , 28+
Find the indicated quantities for the appropriate sequences.an = 49/8, r = −2/7, Sn = 1911/32, a1 = ?
Find the first four terms of the indicated expansions.(x1/2 − 4y)12
Find the first four terms of the indicated expansions. B2 + 1 26 20
Find the fractions equal to the given decimals.0.0273273273 . . .
Find any of the values of a1, r, an, n or Sn that are missing.1/16, 1/4, 1, . . ., 64
Find the indicated quantities for the appropriate sequences.a1 = 80, an = −25, Sn = 220, d = ?
Find the first four terms of the indicated expansions. (2x² + 3 15
Find the first four terms of the indicated expansions.(2a − x−1)11
Find the fractions equal to the given decimals.0.82222 . . .
Find any of the values of a1, r, an, n or Sn that are missing.5, 1, 0.2, . . . , 0.00032
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence. d = −3, n = 3, a3 = −5.9
Find the indicated quantities for the appropriate sequences.a6 = 3, d = 0.2, n = 11, S11 = ?
When two dice are rolled repeatedly, the probability of rolling a sum of 6 before a sum of 7 isFind this probability. 5 25 ਤੱਕ + ( 36 ) ਤੱਕ + ( 3% ) ਤੱਕ + ( 3% ) ਤੱਕ
Find the fractions equal to the given decimals.0.1181818 . . .
Find any of the values of a1, r, an, n or Sn that are missing.r = 3/2, n = 5, S5 = 211
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence.d = 3, n = 30, S30 = 1875
Find the indicated quantities for the appropriate sequences.n = 6, r = −0.25, S6 = 204.75, a6 = ?
Find the fractions equal to the given decimals.0.3336336336 . . .
Find any of the values of a1, r, an, n or Sn that are missing.r = −1/2, an = 1/8, n = 7
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence.d = 9, n = 18, S18 = 1521
Find the indicated quantities for the appropriate sequences.a1 = 10, r = 0.1, Sn = 11.111, n = ?
Approximate the value of the given expression to three decimal places by using three terms of the appropriate binomial series. Check using a calculator.1.056
Find any of the values of a1, r, an, n or Sn that are missing.an = 27, n = 4, S4 = 40
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence.a1 = 7.4, d = −0.5, an = −23.1
Find the indicated quantities for the appropriate sequences.a1 = −1, an = 32, n = 12, S12 = ? (arith)
Approximate the value of the given expression to three decimal places by using three terms of the appropriate binomial series. Check using a calculator.√0.927
Solve the given problems by use of an appropriate sequence or series. All numbers are accurate to at least two significant digits.Approximate 3√29.7 by using the method of Exercise 61.Data from
Find any of the values of a1, d, an, n, or Sn that are missing for an arithmetic sequence. 41 -2, 2 = 19, 419 36
Explain why there is no infinite geometric series with a1 = 5 and S = 2.
Find any of the values of a1, r, an, n or Sn that are missing.a1 = 3, n = 7, a7 = 192
Find the indicated quantities for the appropriate sequences.a2 = 800, an = 6400, Sn = 32, 500, d = 700, n = ? (arith.)
Approximate the value of the given expression to three decimal places by using three terms of the appropriate binomial series. Check using a calculator.3√1.045
Liquid is continuously collected in a wastewater-holding tank such that during a given hour only 92.0% as much liquid is collected as in the previous hour. If 28.0 gal are collected in the first
Find any of the values of a1, r, an, n or Sn that are missing.a2 = 15, r = 1/5, an = 3/625
Find the indicated quantities for the appropriate arithmetic sequence.a6 = 560, a10 = 720 (find a1, d, Sn for n = 10 )
Find the sums of the given infinite geometric series.0.9 + 0.6 + 0.4 + . . .
Approximate the value of the given expression to three decimal places by using three terms of the appropriate binomial series. Check using a calculator.0.98−7
If 75% of all aluminum cans are recycled, what is the total number of recycled cans that can be made from 400,000 cans that are recycled over and over until all the aluminum from these cans is used
Find any of the values of a1, r, an, n or Sn that are missing.r = −2, n = 6, S6 = 42
Find the indicated quantities for the appropriate arithmetic sequence.a17 = − 91, a2 = −73 (find a1, d, Sn for n = 40 )
Find the sums of the given infinite geometric series.1280 − 320 + 80 − . . .
Find the first four terms of the indicated expansions by use of the binomial series.(1 + x)8
The amounts of plutonium-237 that decay each day because of radioactivity form a geometric sequence. Given that the amounts that decay during each of the first 4 days are 5.882 g, 5.782 g, 5.684 g,
Find the indicated quantities for the appropriate arithmetic sequence.Is ln 3, ln 6, ln 12, . . . an arithmetic sequence? Explain. If it is, what is the fifth term?
Is 3, 3x+1, 32x+1, . . . a geometric sequence? Explain. If it is, find a .
Find the sums of the given infinite geometric series.1 + 1.02−1 + 1.02−2 + . . .
Find the first four terms of the indicated expansions by use of the binomial series.(1 + x)−1/3
A helium-filled balloon rose 120 ft in 1.0 min. Each minute after that, it rose 75% as much as in the previous minute. What was its maximum height?
Find the indicated quantities for the appropriate arithmetic sequence.Is sin 2°, sin 4°, sin 6°, . . . an arithmetic sequence? Explain. If it is, what is the fifth term?
Show that a, √ab, b are three successive terms of a geometric sequence (a > 0, b > 0).
Find the sums of the given infinite geometric series.3 − √3 + 1 − . . .
Find the fractions equal to the given decimals.0.030303 . . .
Find the first four terms of the indicated expansions by use of the binomial series.(1 − 3x)−2
After beginning to coast, a bicyclist travels 10 m during the first second and then travels 90% as far each second as in the previous second. How far does the bicycle travel while coasting?
Find the indicated quantities for the appropriate arithmetic sequence.Find a formula with variable n for the nth term of the arithmetic sequence with a1 = 3 and an +1 = an + 2 for n = 1, 2, 3,
Find the first four terms of the indicated expansions by use of the binomial series. 1 √1-x
A square has sides of 20 cm. Another square is inscribed in the first square by joining the midpoints of the sides. Assuming that such in scribed squares can be formed endlessly, find the sum of the
Find x if 2, 6, 2x + 8 are successive terms of a geometric sequence.
Find the fractions equal to the given decimals.0.363363 . . .
Find the first four terms of the indicated expansions by use of the binomial series. x + 1/
Find the first four terms of the indicated expansions by use of the binomial series.(1 − 2√x)9
If a major league baseball team can make it to the World Series, it can be a great financial boost to the economy of their city. Let us assume, if their team plays in the World Series, that tourists

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