Question
Let there be an A.P. with first term ' $a$ ', common difference ' $d$ '. If $a_n$ denotes in $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find.
$S _{22}$, if $d =22$ and $a _{22}=149$
$S _{22}$, if $d =22$ and $a _{22}=149$
✓
Answer
Given $d =22, a _{22}=149, n =22$
We know that
$a_n=a+(n-1) d$
$149=a+(22-1) 22$
$149=a+462$
$a=-313$
Now, Sum is given by
$S_{n}=\frac{n}{2}[2 a(n-1) d]$
Where; a = first term for the given A.P.
$d = common$ difference of the given A.P.
$n =$ number of terms
So, using the formula for $n =22$, we get
$\left.S_{22}=\frac{22}{2}\{2 \times(-313)+(22-1) \times 22)\right\}$
$S_{22}=11\{-626+462\}$
$S_{22}=-1804$
Hence, the sum of $22$ terms is $-1804$ .
We know that
$a_n=a+(n-1) d$
$149=a+(22-1) 22$
$149=a+462$
$a=-313$
Now, Sum is given by
$S_{n}=\frac{n}{2}[2 a(n-1) d]$
Where; a = first term for the given A.P.
$d = common$ difference of the given A.P.
$n =$ number of terms
So, using the formula for $n =22$, we get
$\left.S_{22}=\frac{22}{2}\{2 \times(-313)+(22-1) \times 22)\right\}$
$S_{22}=11\{-626+462\}$
$S_{22}=-1804$
Hence, the sum of $22$ terms is $-1804$ .
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