Question

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Answer 1

Let the given AP contain n terms.
Here a = 7, l = 49 and `S_(n) = 420.`
`therefore S_(n) = (n)/(2) (a+l)`
`therefore (n)/(2)(7+49) = 420 rArr (n)/(2) xx 56 = 420`
`rArr 28n = 420 rArr n = (420)/(28) = 15.`
Thus, the given AP contains 15 terms and `T_(15) = 49.`
Let d be the common difference of the given AP. Then,
`T_(15) = 49 rArr a + 14d = 49`
`rArr 7 + 14d = 49`
`rArr 14d = 42 rArr d = 3.`
Hence, the common difference of the given AP is 3.