Question

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

Answer 1

Answer:

1661

Step-by-step explanation:

Given:

d=7

22nd term=149

To find:

sum of first 22 terms

solution:

22nd term =a+21d=149

putting value of d=7 we get

a+(21*7)=149

a+147=149

a=2

sum=n/2(2a+(n-1)d)

sum of first 22 terms=

=22/2(2*2+(22-1)7)

=11(4+147)

=11*151

=1661

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

d = 7 (Common difference)

$\rightarrow{a_{22}=149}$

a + (22 - 1)d = 149

a + 21 × 7 = 149

a + 147 = 149

a = 149 - 147

a = 2

★Now sum of 22 terms :-

★Substitute the values :-

n = 32 , a = 2 and d = 7

${\boxed{\sf\:{S_{n}=\dfrac{n}{2}[2a+(n-1)d]}}}$

${\boxed{\sf\:{S_{22}=\dfrac{22}{2}[2(2)+(22-1)7]}}}$

= 11(4 + 21 × 7)

= 11(4 + 147)

= 11 × 151

= 1661

★Therefore :-

$\fbox{Sum\;of\;first\;22\;term\;is\;1661}$