Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. -7th term is 29; 15th term is -27 A) a1 = 78, d = 7, a_n = a_n- 1 + 7 B) a1 = 71, d = -7, a_n = a_n- 1 - 7 C) a1 = 71, d = 7, a_n = a_n- 1 + 7 D) a1 = 78, d = -7, a_n = a_n- 1 - 7

Question

Quizplus · Accepted Answer

Given the 7th term is 29 and the 15th term is -27, we can set up two equations based on the formula for the nth term of an arithmetic sequence, $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. For the 7th term, $29 = a_1 + 6d$, and for the 15th term, $-27 = a_1 + 14d$. Solving these equations simultaneously gives $a_1 = 71$ and $d = -7$. The recursive formula for an arithmetic sequence is $a_n = a_{n-1} + d$, so the correct recursive formula with these values is $a_n = a_{n-1} - 7$.

Find the First Term, the Common Difference, and Give a Recursive