Find the first term, the common difference, and give a recursive formula for the arithmetic sequence.
-6 th term is $- 17 ; 15$ th term is $- 53$
A) $a _ { 1 } = 3 , d = - 4 , a _ { n } = a _ { n - 1 } - 4$
B) $a _ { 1 } = 3 , d = 4 , a _ { n } = a _ { n - 1 } + 4$
C) $a _ { 1 } = 7 , d = 4 , a _ { n } = a _ { n - 1 } + 4$
D) $a _ { 1 } = 7 , d = - 4 , a _ { n } = a _ { n - 1 } - 4$

Question

Quizplus · Accepted Answer

The common difference $d$ can be found using the formula $a_n = a_1 + (n - 1)d$. Substituting the given terms, $a_6 = -17$ and $a_{15} = -53$, we can form two equations: $-17 = a_1 + 5d$ and $-53 = a_1 + 14d$. Solving these simultaneously gives $a_1 = 3$ and $d = -4$. The recursive formula for an arithmetic sequence is $a_n = a_{n-1} + d$, which becomes $a_n = a_{n-1} - 4$ for this specific sequence.

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