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# Find the Sum of First 22 Terms of an A.P. in Which D = 22 and a = 149. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Questions

Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.

Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.

$S_{22} , \text{ if } d = 22 \text{ and } a_{22} = 149$

#### Solution 1

Given d = 22,

$a_{22} = 149$

We know that

an = a + (n-1)d

$149 = a + (22 - 1)22$
$149 = a + 462$
$a = - 313$

Now, Sum is given by

S_n = n/2 [2a +(n-1)d]

Where; a = first term for the given A.P.

d = common difference of the given A.P.

= number of terms

So, using the formula for n = 22, we get

$S_{22} = \frac{22}{2}\left\{ 2 \times \left( - 313) + (22 - 1) \times 22 \right) \right\}$
$S_{22} = 11\left\{ - 626 + 462 \right\}$
$S_{22} = - 1804$

Hence, the sum of 22 terms is −1804.

#### Solution 2

Given 22nd term, a_22 = 149 and difference d = 22

we know a_n = a + (n - 1)d

22 nd term, a_22 = a + (22 - 1)d

=> 149 = a + 21 xx 22

=> a = 149 - 462

=> a = - 313

We know, sum of n terms

S_n = n/2 [2a + (n - 1)d]

=> S_22 = 22/2[2(-313) + (22 - 1)22]

=> S_22 = 11[-626 + 21 xx 22]

=> S_22 = 11[-626 + 462]

=> S_22 = 11 xx -164

=> S_22 = -1804

Hence sum of 22 terms -1804

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Solution Find the Sum of First 22 Terms of an A.P. in Which D = 22 and a = 149. Concept: Sum of First n Terms of an AP.
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