Find the first six terms of the sequence.

a₁= -6, a_n= 4 a_n-1

Find an equation for the nth term of the arithmetic sequence.

-15, -6, 3, 12, ...

Find an equation for the nth term of the arithmetic sequence.

a₁₄= -33, a₁₅= 9

Determine whether the sequence converges or diverges. If it converges, give the limit. (1 point)

48, 8,4/3,2/9, ...

Find an equation for the nth term of the sequence.

-3, -12, -48, -192, ...

Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.

Write the sum using summation notation, assuming the suggested pattern continues.

5 - 15 + 45 - 135 + ..

Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 3 + 3 + 9 + ... + 81

Write the sum using summation notation, assuming the suggested pattern continues.

64 + 81 + 100 + 121 + ... + n²+ ...

Find the sum of the geometric sequence. (1 point)

1,1/2,1/4,1/8,1/16

Use mathematical induction to prove the statement is true for all positive integers n.

The integer n³+ 2n is divisible by 3 for every positive integer n.

A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.