1.

The sum of the 4th and 8th terms of an AP is 24 and the sum of its 6th and 10th terms is 44. Find the first terms of the AP.

Answer» Let a be the first term and d be the common difference of the given AP. Then,
`T_(4) + T_(8) = 24 rArr (a+ 3d) + (a+7d) = 24`
`rArr 2a+ 10d = 24`
` rArr a + 5d = 12 " "…(i)`
and `T_(6) +T_(10) = 44 rArr (a + 5d) + (a+ 9d) = 44`
`rArr 2a +14d = 44`
`rArr a + 7d = 22. " "....(ii)`
On solving (i) and (ii), we get a = -13 and d = 5.
`therefore` first three terms of the given AP are -13, -8 and -3.


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