Question

If the sum of the first 2n terms of 2, 5, 8. Is equal to the sum of the first n terms of 57, 59, 61., then n is equal to

Answer 1

in first AP,

n =2n

a=2

d = 3

Sn = 2n/2 (4 +(2n-1)3)

= n ( 4+ 6n -3)

= n( 1+6n)

= n +6n2

for 2nd AP,

n = n

a =57

d = 2

Sn = n/2 (114 +(n-1)2)

= n/2 (114 +2n -2)

= n/2(112+2n)

= 56n +n2

since it is given ,

S2n =Sn

n+6n2 = 56n +n2

5n2 = 55n

n2 = 11n

n2 -11n =0

n(n-11) =0

=> n =0 and n =11

HOPE THIS HELPS..