Question

find the sum of first 22 terms of an ap in which d=7 and 22nd term is 149.​

Answer 1

SOLUTION

Given

• d= 7
• 22nd term is 149

Answer

• Sum of first 22 term = 1661

To Calculate

• Sum of first 22 terms __?

Step by Step Explanation

Where

Common difference (d) = 7

22nd term = 149

an = a+(n-1)×d

==> 149= a+(22-1)×d

==> 149= a+21d

==> 149= a+21×7

==> 149=a+147

==> 149-147=a

==> a= 2

Sn = n/2(2a+(n-1)×d)

==> S22 = 22/2(2×2+(22-1)×7)

==> S22 = 11 ( 4+21×7)

==> S22= 11×151

==> S22= 1661

Hence

• Sum of first 22 terms = 1661

_______________________________

Answer 2

Solution

Given That :-

• Common different d = 7
• 22nd term be = 149

Find :-

• Sum of 22 terms

Explanation

We Have,

★ an = a + (n-1)d

★ Sn = n/2[ 2a + (n-1)d]

So,

➡ 149 = a + (22-1)×7

➡a = 149 - 21×7

➡a = 149 - 147

➡a = 2

So, Now calculate Sum of 22 terms

➡ S22 = 22/2[2×2 + (22-1)×7]

➡S22 = 11[4 + 21×7]

➡S22 = 11[4 + 147]

➡S22 = 11 × 151

➡S22 = 1661

Hence

• Sum of 22 terms of A.P. series = 1661