Q. 354.5( 11 Votes )

Find an A.P

Let a be the first term and d be the common difference.

Given: a4 = 9

a6 + a13 = 40

We first find the common difference.

Now, Consider a4 = 9

a + (4 – 1)d = 9

a + 3d = 9 ……………………….(1)

Consider a6 + a13 = 40

a + (6 – 1)d + a + (13 – 1)d = 40

2a + 17d = 40 ………………..(2)

Subtracting twice of equation (1) from equation (2), we get,

11d = 22

d = 2

Common difference = d = 2

Put the value of d in equation (), we get

a = 9 – 3d

= 9 – 6

= 3

a = 3

The AP will be a, a + d, a + 2d, a + 3d,…

Thus the AP will be 3, 5, 7, 9,…

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