Q. 164.0( 2 Votes )

# The sum of the 5<

Answer :

Given the sum of the 5th and 9th terms of an AP is 30.

We know that the nth term of an AP, an = a + (n – 1) d.

a5 = a + (5 – 1) d = a + 4d

a9 = a + (9 – 1) d = a + 8d

As given, a + 4d + a + 8d = 30

2a + 12d = 30 … (1)

Also given 25th term is three times its 8th term.

a25 = a + (25 – 1) d = a + 24d

a8 = a + (8 – 1) d = a + 7d

As given, a + 24d = 3 (a + 7d)

a + 24d = 3a + 21d

-2a + 3d = 0 … (2)

Solving the (1) and (2) equations,

15d = 30

d = 2

Substituting d = 2 in (2),

-2a + 6 = 0

6 = 2a

a = 3

Now, we got the first term, a = 3 and the common difference, d = 2,

The AP is as follows: 3, 5, 7, 9, …

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