Question

Question 7 Find the sum of first 22 terms of an AP in which d = 7 and 22 nd term is 149.

Class 10 - Math - Arithmetic Progressions Page 113

Answer 1

Sn=n/2[2a+(n-1)d]----
given that 22nd term is 149
a+21d=149
a=149-147
a=2(substituting in formula)
s22=22/2[2(2)+(22-1)7]
=11(4+147)
=11(151)
=1661
therefore sum of first 22terms =1661

Answer 2

Sum of n terms of an AP

The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by

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

Sn=n /2 [ a + l ]       (l = an= last term)
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Solution:

Given:

d = 7
a22 = 149

S22 = ?

an = a + (n − 1)d

a22 = a + (22 − 1)d
149 = a + 21 × 7
149 = a + 147
149 -147 = a
a = 2

Sn = n/2 (a + an)

= 22/2 (2 + 149)
= 11 × 151
S22= 1661

The sum of first 22 terms of an AP is (S22)= 1661

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hope this will help you....