Math, asked by sanskar8234, 11 months ago

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

Find the sum of first 19 terms of this progression.

Answers

Answered by MaheswariS
0

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}

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