Question

if the sum of first 7 terms of an AP is 49 and that of 17 terms is 289 find the sum of first 11 terms.
​

Answer 1

Answer:

Given  

S  

7

​  

=49 and S  

17

​  

=289

By using S  

n

​  

=  

2

n

​  

[2a+(n−1)d] we have,

S  

7

​  

=  

2

7

​  

[2a+(7−1)d]=49

⇒49=  

2

7

​  

[2a+(7−1)d]

⇒49=  

2

7

​  

(2a+6d)

⇒7=a+3d

⇒a+3d=7...................(i)

S  

17

​  

=  

2

17

​  

[2a+(17−1)d]=289

⇒289=  

2

17

​  

[2a+(17−1)d]

⇒289=  

2

17

​  

(2a+16d)

⇒17=a+8d

⇒a+8d=17......................(ii)

Substituting (i) from (ii), we get

5d=10 or d=2

From equation (i),

a+3(2)=7

a+6=7 or a=1

S  

n

​  

=  

2

n

​  

[2(1)+(n−1)2]

=  

2

n

​  

[2+(n−1)2]

=  

2

n

​  

(2+2n−2)=n  

2