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The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.

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Given:

a5 = 22

a + 4d = 22 (i)

Acc. to question,

a9 = 6a2 (ii)

a= a +8d

a= a+d

Putting the value of a9 and a2 in (ii)

a +8d = 6(a +d)

2d = 5a

2d = 5(22 - 4d)

22d = 110

d = 5

Now, putting the value of d in (i)

a = 22 - 4(5) = 2

a1 = a = 2

a2 = a +d = 2 +5 = 7

a3 = a +2d = 2 + 2(5) = 12

Hence, the A.P. is 2, 7, 12, 17,..........

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