Question

the sum of 15 terms of an arithmetic sequence with common difference 6 is 780.write the algebric expression of the sequence
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Answer 1

$\huge\sf\purple{\underline{\underline{\pink{Ans}\red{wer:}}}}$

$\sf{The \ required \ sequence \ is \ 10, \ 16, \ 22,...}$

$\sf\orange{Given:}$

$\sf{In, \ an \ AP,}$

$\sf{\leadsto{Sum \ of \ 15 \ terms(S_{15})=780}}$

$\sf{\leadsto{Common \ difference (d)=6}}$

$\sf\pink{To \ find:}$

$\sf{The \ sequence.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Here, \ d=6, \ S_{15}=780}$

$\boxed{\sf{S_{n}=\dfrac{n}{2}[2a+(n-1)d]}}$

$\sf{\therefore{S_{15}=\dfrac{15}{2}[2a+(15-1)\times6]}}$

$\sf{\therefore{780=\dfrac{15}{2}[2a+14\times6]}}$

$\sf{\therefore{780=15(a+7\times6)}}$

$\sf{\therefore{a+42=\dfrac{780}{15}}}$

$\sf{\therefore{a+42=52}}$

$\sf{\therefore{a=52-42}}$

$\sf{\therefore{a=10}}$

$\sf{The \ required \ sequence \ is}$

$\sf{t_{1}=a=10,}$

$\sf{t_{2}=a+d=10+6=16,}$

$\sf{t_{3}=a+2d=10+2(6)=22.}$

$\sf\purple{\tt{\therefore{The \ required \ sequence \ is \ 10, \ 16, \ 22,...}}}$