Question

the sum of the first 13 terms of an ap is 416.find its 7th term​

Answer 1

Answer:

$a_{7}$ = 32

Step-by-step explanation:

The nth term of an A.P

$a_{n}$ = a+(n-1)d

Given;

We need to find the 7th term;

$n_{7}$ = a + (7-1)d

$n_{7}$ = a + 6d

Sum of n terms $S_{n}$ = n/2 * [2a + (n-1)d]

Given; Sum $S_{n}$ = 416

=> 416 = 13/2 * [2a + (13-1)d]

=> 416 = 13/2 * [2a + 12d]

=> 416 = 13/2 * 2 * [a + 6d]

=> 416 = 13/2 * 2 * $a_{7}$

=> $a_{7}$ = (416 * 2)/26

                  = 32