Formula for the nth term of an Arithmetic sequence. an = a, +d(n-1) where an is the nth term a, is the first term d is the common difference n is the number of termsFormula for the nth term of an Arithmetic sequence. an = a, +d(n-1) where an is the nth term a, is the first term d is the common difference n is the number of terms 1 DHow do we get the common difference using the alternative formula? Example 3: Find the common difference of the arithmetic sequence whose a, is 8 and whose a16 is 47.1L 1.9L v: vL -/. How do we get the common difference using the alternative formula ? Ginale d= nk d_478 _163 d_39 '13 d=3 Formula for finding the arithmetic series Formula 1: n S n (a1 tan) 2 * If the nth term/ last term is given.Illustrative Examples: Find the sum of the given arithmetic sequence: 17, 22, 27, 32, 37, 42 n Sn : 5011 + an) 6 56 E(17 + 42) 56 = 3(59) S6 = 177 Formula for finding the arithmetic series Formula 2: n Sn = NI 2a1+ d(n - 1) * If the nth term/ last term is NOT given.Illustrative Examples: 1. Find the sum of the given arithmetic sequence: 2, 5, 8, 11, . . . 20th term n Sn = 2 [2a + d(n-1)] 20 S20 = 2 [2(2)+ 3(20-1)] S20 = 10 [4+ 3(19)] S20 = 10(4+ 57) S20 = 10(61) S20 = 610Activity 1: Find the indicated term of the arithmetic sequence and the series with the given conditions. I. = 17,d = 5,a7 2?,57 =? : _3,d 2 7, C112 2?,520 Z? 1 a1 = 3,61 25,618 2?,515 2? (14 = 43,619 = 22, Q15 2?,515 :? a3 : 143C137 : 2,a5 2?,520 2