Question

The sum of first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term

Answer 1

s7=63 s14=161 to find a28=?

Answer 2

Answer:

56

Step-by-step explanation:

Using S = (n/2) [2a + (n - 1)d]   ,where letters have their usual meaning.

 For first 7 terms:

⇒ 63 = (7/2) [2a + (7 - 1)d]

⇒ (63 * 2)/7 = [2a + 6d]

⇒ 18 = 2a + 6d  

⇒ 9 = a + 3d      ⇒ 9 - 3d = a

 For next 7 terms:

⇒ 161 = (7/2) [8th term + 14th term]

⇒ (161 x 2)/7 = [a + 7d + a + 13d]

⇒ 46 = 2a + 20d

⇒ 23 = a + 10d

⇒ 23 = 9 - 3d + 10d       [from above]

⇒ 2 = d

  thus, a = 9 - 3(2) = 3

∴ 28th term = a + 27d

                    = 3 + 27(2)

                    = 56