Question

the sum of first 7 terms ofan arithmetic sequence is119 and the sum of the first 11 terms is 275.what is the Fourth term​

Answer 1

Answer:

The fourth term is 17

Step-by-step explanation:

Given that the sum of the first 7 terms of an arithmetic sequence is 119 and the sum of the first 11 terms is 275. The question is to find the fourth term.

The formula to find the $n^{th}$ term is given as,

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

Here, we want to find the fourth term. That is, n = 4

          $a_{n}=a+\left( 4-1\right) d\\\\a_{n}=a+3 d$

The formula to find the sum of n terms is given as,

            $S_{n}=\dfrac{n}{2}\left( 2a+\left( n-1\right) d\right)$

Therefore we can write the given sum of the first 7 terms as,

          $\begin{aligned}S_7=\dfrac{7}{2}\left(2a+\left(1-1\right)d\right)\\119=\frac{7}{2}\left(2a+6d\right)\\=\frac{7}{2}\times2\left(a+3d\right)\\119=7\left(a+3d\right)\end{aligned}$

                 $a+3d=\dfrac{119}{7} \\\\a+3d=17$

We know that a+3d is the fourth term of the arithmetic sequence. Therefore the fourth term is 17.