Answer to Question #245565 in Calculus for Anne

Question

Find a17 of arithmetic sequence (2,-24,-50,-76)

Answer 1

Arithmetic sequence nth theorem formula

$a_n=a_1+(n-1)d\\ a_6=24=a_1+(6-1)d \implies a_1+5d=24......(1)\\ a_{11}=39=a_{11}+(11-1)d \implies a_1+10d=39......(2)\\ Adding \space 1 \& 2\\ d= 3\\ a_1=9\\ So, a_{17}=9+(17-1)*3=57$