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

  Common difference = +3

Step-by-step explanation:

(i) Given:  first and the last terms of an AP are 7 and 49 respectively. sum of all its terms is 420

Find: d

Solution:  

  a = 7

  an = 49 = a + (n-1)d

  Sum = 420

  n/2 (2a + (n-1)d) = n/2 (a + a + (n-1)d) = n/2 (a +an)

  So we have n/2 (a +an) = 420

   n/2 (7 +49) = 420

   n/2 (56) = 420

  Therefore n = 420 *2 / 56 = 15

  Substituting n=15 in an, we get 49 = 7 + 14d

  14d = 42

  Therefore d = 42/14 = +3

  Common difference = +3