Question

Two A.P. have the same common difference. If the first terms of the A.P.s are 5 and 6 respectively, find the difference between the sum of their first 20 terms.

Answer 1

Let the common difference be d

First AP

5, 5+d, 5 + 2d.......

S20 = 20/2 [ 2× 5 + (20-1)d]

S20 = 10 [ 10 + 19d]

S20 = 100 + 190d ---------(1)


Second AP

6, 6+d, 6+2d......

S' 20 = 20/2[ 2 × 6 + (20-1)d]

S' 20 = 10 [ 12 + 19d]

S' 20 = 120 + 190d -------(2)

On Subtracting equation 1 from 2, we get

S' 20 - S20 = 120 + 190d - 100 - 190d

S' 20 - S20 = 20

Answer 2

•1st Case

T1 = 5

a=5

S20=20/2[2a+(19)d]
S20=10[10+19d]
S20=100+190d-------------------(i)

•2nd Case

T1=6

a=6

S20=10[12+19d]
S20=120+190d---------------------(ii)

Subtract equation (i) from (ii)
Difference bet^n Sums = 20 [Ans}