Question

the sum of the 5 and 9 term of an ap is 30.if it 8 term is three time its 25 term find ap

Answer 1

Solution:

Given sum of 5th term and 9th term of AP=30

a+4d + a+8d =30

2a + 12 d = 30 ---equation (1)

Given that 25 term is three times of 3rd term in AP

25th term= 3 (8th term)

( a+ 24d)= 3(a +7d)

a+ 24d = 3a+ 21d

24d - 21 d= 3a- a

3d = 2a --- equation 2

Substitute the value of 2d in equation (1) we get

2a+ 12d = 30

3d +12d =30

15d =30

d = 2

2a = 3d

2a= 3x 2

2a= 6

a=3

THEREFORE AP is 3, 5,7, 9..

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