Question

The sum of first 8term of an AP is 100 and of first 19term is551 find the sum offirst 25 term

Answer 1

Answer:

S₂₅=950

Step-by-step explanation:

Given:-

S₈=100,S₁₉=551

To Find:-

S₂₅

Formula Applied:-

Sₙ=n/2[2a+(n-1)d]

Solution:-

S₈=8/2[2a+(8-1)d]

100=4(2a+7d)

2a+7d=100/4

2a+7d=25-------------(1)

S₁₉=19/2[2a+(19-1)d]

551/19=1/2[2a+18d]

29×2=2a+18d

2a+18d=58----------------(2)

Subtracting Equation(2) from Equation(1):-

2a-2a+18d-7d=58-25

11d=33

d=33/11

d=3

2a+7d=25

2a=25-7(3)

2a=25-21=4

a=4/2

a=2

Now,

S₂₅=25/2[2(2)+(25-1)(3)]

S₂₅=25/2[4+(24)(3)]

S₂₅=25/2(72+4)=(25/2)×76

S₂₅=25×38

S₂₅=950