Q. 184.5( 6 Votes )

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

Answer :

Given: a_{4} + a_{8} = 24 …(i)

a_{6} + a_{10} = 34 …(ii)

a_{4} = a + 3d

a_{8} =a + 7d

a_{6} =a + 5d

a_{10}=a + 9d

Put the value of a_{4} and a_{8} in (i)

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

a + 5d =12 …(iii)

Put the value of a_{6} and a_{10} 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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