Question

The sum of the first 3 terms of an AP is 21and the last 3 terms is 276. then find the sum of first 20 terms​

Answer 1

Answer:

S20 = 990.

Step-by-step explanation:

a+(a+d)+(a+2d) = 21

3a+3d = 21 ------------1

(a+17d)+(a+18d)+(a+19d) = 276

3a+54d = 276---------2

By solving equation 1 and 2,

3a+ 3d = 21

3a+54d = 276

= 51d = 255

d = 255/51

d = 5.

Put d=5 in equation 1,

3a+3d = 21

3a+3(5) = 21

3a+15 = 21

3a = 21-15

3a = 6

a = 6/3

a = 2.

S20 = ?

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

= 20/2 ( 2×2+(20-1)5 )

= 10 ( 4+95 )

= 10 ( 99 )

= 990.