Question

for an A.P if first term is 8 and common difference is 8 then find Sn
​

Answer 1

Answer:

Let S

n

be the sum of n terms of an AP with first term a=8 and common difference d=20. Then,

S

n

=

2

n

(2a+(n−1)d)⇒S

n

=

2

n

(2×8+(n−1)×20)⇒S

n

=

2

n

(16+20n−20)

⇒S

n

=

2

n

(20n−4) ...1

similarly Let S

2n

be the sum of 2n terms of an AP with first term a1=30 and common difference d1=8. Then,

S

2n

=

2

2n

(2a1+(2n−1)d1)⇒S

2n

=

2

2n

(2×30+(n−1)×8)⇒S

2n

=

2

2n

(60+8n−8)

⇒S

2n

=n(8n+52) ...2

According to question S

n

=S

2n

2

n

(20n−4)=n(8n+52)

⇒10n−2=8n+52

⇒2n=54

⇒n=27