Question

The twenty-first term of an ap is 37 and the first twenty term is 320,what is the sum of the first ten term?

Answer 1

Answer:

answer is in the attachment

hope it helps you

Answer 2

Given info : The twenty first term of an AP is 37 and the sum of first twenty terms 320.

To find : the sum of first ten terms is..

solution : 21st term = 37

⇒a + (21 - 1)d = 37 , here a is first term and d is common difference of given ap.

⇒a + 20d = 37 ...(1)

again, sum of first twenty terms = 320

using formula, Sn = n/2 [2a + (n - 1)d]

⇒320 = 20/2 [2a + (20 - 1)d]

⇒32 = 2a + 19d ...(2)

from equations (1) and (2)

d = (74 - 32)/21 = 2

and a = 37 - 2 × 20 = -3

now sum of first ten terms = 10/2[2 × -3 + (10 - 1) × 2]

= 5[-6 + 18] = 5 × 12 = 60

Therefore the sum of first ten terms is 60.