# The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.?

Given: a4 + a8 = 24 …(i)

a6 + a10 = 34 …(ii)

a4 = a + 3d

a8 =a + 7d

a6 =a + 5d

a10=a + 9d

Put the value of a4 and a8 in (i)

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

a + 5d =12 …(iii)

Put the value of a6 and a10 in (ii)

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

a +7d =17 …(iv)

Subtracting (iii) from (iv), we get

2d = 5

d =

Putting the value of d in (iii), we get

a = 12 - =

Hence, first term is and common difference is

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