Find the sum:$34 + 32 + 30 + ………. + 10$

Given:

Given sequence is $34 + 32 + 30 + ………. + 10$.

To do:

We have to find the sum of $34 + 32 + 30 + ………. + 10$.

Solution:

Here,

\( 34+32+30+\ldots+10 \) is in A.P.
\( a=34, d=32-34=-2 \) and \( l=10 \)

We know that,

\( a_{n}=a+(n-1) d \)

\( \Rightarrow 10=34+(n-1) \times(-2) \)
\( \Rightarrow 10=34-2 n+2 \)

\( \Rightarrow 2 n=34+2-10=26 \)
\( \Rightarrow n=\frac{26}{2}=13 \)
\( \mathrm{S}_{n}=\frac{n}{2}[a+l] \)

\( =\frac{13}{2}[34+10] \)
\( =\frac{13}{2} \times 44 \)
\( =13 \times 22=286 \)

Therefore, the sum of the given sequence is $286$. 

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Updated on: 10-Oct-2022

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