Q44 of 202 Page 9

The sum of 5^th and 9^th terms of an AP is 30. If its 25^th term is three times its 8^th term, find the AP.

a₅ +a₉=30

(a +4d) + (a +8d)=30

2a +12d=30

a + 6d=15 (i)

Acc. To question,

a₂₅ =3a₈

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

3d=2a

3d=2(15 -6d) [from(i)]

15d=30

d=2

Putting the value of d in (i),

a= 15 – 6(2)=3

a₁ = a=3

a₂ =a +d=3 +2=5

a₃ =a +2d=3 + 2(2)=7

Hence, the A.P. is

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The sum of 5th and 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.