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

Answer:

[tex]a_{7}[/tex] = 32

Step-by-step explanation:

The nth term of an A.P

[tex]a_{n}[/tex] = a+(n-1)d

Given;

We need to find the 7th term;

[tex]n_{7}[/tex] = a + (7-1)d

[tex]n_{7}[/tex] = a + 6d

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

Given; Sum [tex]S_{n}[/tex] = 416

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

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

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

=> 416 = 13/2 * 2 * [tex]a_{7}[/tex]

=> [tex]a_{7}[/tex] = (416 * 2)/26

                  = 32