Question

Given the explicit formula for an arithmetic sequence, find the first five terms and the 52nd term.

An = -10n + 26
A) First five terms: 16, 6, -4, -14, -24; 52nd term: -474
B) First five terms: 16, 26, 36, 46, 56; 52nd term: 746
C) First five terms: 16, 26, 36, 46, 56; 52nd term: 6
D) First five terms: 16, 26, 36, 46, 56; 52nd term: -746

Answer 1

The first five terms of the arithmetic sequence are 16, 6, -4, -14, and -24. The 52nd term is -474.

Step-by-step explanation:

An arithmetic sequence is a sequence where each term is obtained by adding a constant difference to the previous term. The explicit formula for an arithmetic sequence is An = -10n + 26.

To find the first five terms, we substitute values of n from 1 to 5 into the formula.

First term (n = 1): A1 = -10(1) + 26 = 16

Second term (n = 2): A2 = -10(2) + 26 = 6

Third term (n = 3): A3 = -10(3) + 26 = -4

Fourth term (n = 4): A4 = -10(4) + 26 = -14

Fifth term (n = 5): A5 = -10(5) + 26 = -24

To find the 52nd term, we substitute n = 52 into the formula.

52nd term: A52 = -10(52) + 26 = -474