Find the sum:$25 + 28 + 31 + ……….. + 100$

Given:

Given sequence is $25 + 28 + 31 + ……….. + 100$.

To do:

We have to find the sum of $25 + 28 + 31 + ……….. + 100$.

Solution:

Here,

\( 25+28+31+\ldots+100 \) is in A.P.

\( a=25, d=28-25=3 \) and \( l=100 \)

We know that,

\( a_{n}=a+(n-1) d \)
\( \Rightarrow 100=25+(n-1) \times 3 \)
\( \Rightarrow 100=25+3 n-3 \)

\( \Rightarrow 100-25+3=3 n \)
\( \Rightarrow 3 n=78 \)

\( \Rightarrow n=\frac{78}{3}=26 \)
\( \mathrm{S}_{n}=\frac{n}{2}[a+l] \)

\( =\frac{26}{2}[25+100] \)
\( =13 \times 125 \)
\( = 1625 \) 

Therefore, the sum of the given sequence is $1625$.  

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Updated on: 10-Oct-2022

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