Question

Sum of n term of ap whose n term is ( 5n+1)

Answer 1

$\red{\underline{\underline{Answer:}}}$

$\sf{The \ sum \ of \ n \ terms \ is \ \frac{n}{2}[5n+7]}$

$\orange{\underline{\underline{Given:}}}$

$\sf{\implies{tn=(5n+1)}}$

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

$\sf{Sum \ of \ n \ n \ terms}$

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

$\sf{\implies{tn=(5n+1)}}$

$\sf{\implies{t1=5(1)+1}}$

$\sf{\implies{t1=6}}$

$\sf{Sn=\frac{n}{2}[t1+tn]...formula}$

$\sf{Sn=\frac{n}{2}[6+5n+1]}$

$\sf{\therefore{Sn=\frac{n}{2}[5n+7]}}$

$\sf\purple{\tt{\therefore{The \ sum \ of \ n \ terms \ is \ \frac{n}{2}[5n+7]}}}$

Answer 2

$\huge\mathfrak\red{\underline{\underline{Question:}}}$

$\rm{Find \ the \ sum \ of \ n \ terms \ of \ AP \ whose \ n }$

$\rm{term \ is \ (5n+1) }$

__________________________________________

$\huge\mathfrak\blue{\underline{\underline{Answer:}}}$

$\rm\green{Sum \ of \ n \ terms \ of \ an \ AP : \frac{n}{2} [5n + 7]}$

__________________________________________

$\sf\large\underline\pink{Given:}$

$\rm{n \ term \ of \ AP \ (5n+1)}$

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

$\rm{Sum \ of \ n \ terms}$

$\huge\mathfrak\green{\underline{\underline{Solution:}}}$

$t(n) = (5n + 1)$

$\rm{Put \ n=1}$

$t(1) = (5(1) + 1) = 6$

$t(1) = 6$

$\rm{we know, }$

$\rm{Sum \ of \ n \ terms \ of \ an \ AP }$

⇛$s(n) = \frac{n}{2} [t(1) + t(n)]$

⇛$s(n) = \frac{n}{2} [6 + (5n + 1)]$

⇛$s(n) = \frac{n}{2} [5n + 7]$

$\rm\orange{Sum \ of \ n \ terms \ of \ an \ AP : \frac{n}{2} [5n + 7] }$

$\rm{Hope \ it \ helps}$ :))