Question

The sum of the 4^th and the 8^th terms of an A.P. is 24 and the sum of the 6^th and the 10^th terms of the same A.P. is 34. Find the first three terms of the A.P.

Answer 1

Let 'a' be the first term and 'd' be the common difference of the given A.P.

t₄ + t₈ = 24  ...(Given)

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

`=>` 2a + 10d = 24

`=>` a + 5d = 12   ...(i)

And t₆ + t₁₀ = 34  ...(Given)

`=>` (a + 5d) + (a + 9d) = 34

`=>` 2a + 14d = 34

`=>` a + 7d = 17  ...(ii)

Subtracting (i) from (ii), we get

2d = 5

`=> d = 5/2`

`=> a + 5 xx 5/2 = 12`

`=> a + 25/2 = 12`

Thus we have,

1^st term = `-1/2`

2^nd = a + d

= `-1/2 + 5/2`

= 2

3^rd term = a + 2d

= `-1/2 + 2 xx 5/2`

= `-1/2 + 5`

= `9/2`