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

The firstand the last terms of an AP are 7 and 49 respectively. If sum

1.	The firstand the last terms of an AP are 7 and 49 respectively. If sum of all itsterms is 420, find its common difference.
Answer» 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.