Question

13. The sum of forth and sixteenth term of an A.P.is 8

Find the sum of first 19 terms of this progression.
​

Answer 1

Answer:

The sum of the first 19 terms of the A.P is 152

Step-by-step explanation:

Given:

$t_4+t_{16}=8$

$\implies\:(a+3d)+(a+15d)=8$

$\implies\:2a+18d=8$

$\implies\:a+9d=8$

Sum of first n terms of the A.P

$\boxed{\bf{S_n=\frac{n}{2}[2a+(n-1)d]}}$

$S_{19}=\frac{19}{2}[2a+(19-1)d]$

$S_{19}=\frac{19}{2}[2a+18d]$

$S_{19}=\frac{19}{2}(2)[a+9d]$

$S_{19}=(19)[8]$

$\implies\:\boxed{S_{19}=152}$