the sum of the first 13 terms of an ap is 416.find its 7th term
Math
akhil254
Question
the sum of the first 13 terms of an ap is 416.find its 7th term
1 Answer

1. User Answers prettystefina11
Answer:
[tex]a_{7}[/tex] = 32
Stepbystep explanation:
The nth term of an A.P
[tex]a_{n}[/tex] = a+(n1)d
Given;
We need to find the 7th term;
[tex]n_{7}[/tex] = a + (71)d
[tex]n_{7}[/tex] = a + 6d
Sum of n terms [tex]S_{n}[/tex] = n/2 * [2a + (n1)d]
Given; Sum [tex]S_{n}[/tex] = 416
=> 416 = 13/2 * [2a + (131)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