Question

The first term of an arithmetic sequence is 1 and sun of the first four term is 100find the first four terms

Answer 1

Answer:-

$\sf{The \ first \ four \ terms \ are \ 1, \ 17, \ 33}$

$\sf{and \ 49 \ respectively.}$

Given:

1. In an AP,

• First term (a) is 4 .

• Sum of first four terms is 100.

To find:

• First four terms of the AP.

Solution:

$\sf{Here, \ first \ term \ (a)=1,}$

$\sf{Sum \ of \ four \ terms \ (S_{4})=100}$

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

$\sf{\therefore{S_{4}=\frac{4}{2}[2(1)+(4-1)d]}}$

$\sf{\therefore{100=2(2+3d)}}$

$\sf{\therefore{2+3d=\dfrac{100}{2}}}$

$\sf{\therefore{2+3d=50}}$

$\sf{\therefore{3d=50-2}}$

$\sf{\therefore{3d=48}}$

$\sf{\therefore{d=\frac{48}{3}}}$

$\sf{\therefore{d=16}}$

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

$\sf{\leadsto{t_{2}=a+d=1+16=17,}}$

$\sf{\leadsto{t_{3}=a+2d=1+2(16)=33,}}$

$\sf{\leadsto{t_{4}=a+3d=1+3(16)=49}}$

$\sf\purple{\tt{\therefore{The \ first \ four \ terms \ are \ 1, \ 17, \ 33}}}$

$\sf\purple{\tt{and \ 49 \ respectively.}}$