Given a1=28,an=-77 and Sn=-196 in an A.P, find the 10th term and the sum of the first 10 terms.

Answer 1

whats ur answer?

Answer 2

a1 = 28 , an = - 77 , Sn = - 196

Sn = ( n / 2 ) ( a1 + an )

- 196 = ( n / 2 ) ( 28 - 77 )

- 196 = ( n / 2 ) ∙ ( - 49 )

Multiply both sides by - 2

392 = 49 n

n = 392 / 49

n = 8

an = a8 = - 77

a8 = - 77

an = a1 + ( n - 1 ) d

a8 = - 77 = 28 + ( 8 - 1 ) ∙ d

- 77 = 28 + 7 d

- 77 - 28 = 7 d

- 105 = 7 d

d = - 105 / 7 = - 15

a10 = 28 + ( 10 - 1 ) ∙ ( - 15 )

a10 = 28 + 9 ∙ ( - 15 )

a10 = 28 - 135

a10 = - 107