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Arithmetic Progressions — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
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.
$\mathrm{S}_{22}$, if $\mathrm{d}=22$ and $\mathrm{a}_{22}=149$
✓

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
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}(\text{n}-1)\text{d}]$
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
$\text{S}_{22}=\frac{22}{2}\{2\times(-313)+(22-1)\times22)\}$
$\text{S}_{22}=11\{-626+462\}$
$\text{S}_{22}=-1804$
Hence, the sum of $22$ terms is $-1804.$

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