Question

The 13^th term of an A.P. is four times its 3^rd term. If its 5^th term is 16, then find the sum of its first ten terms.

Answer 1

 

 

Let the first term be ‘a’ and the common difference be ‘d’ of the A.P.
t₁₃ = 4t₃
⇒ a + 12d = 4(a + 2d)
⇒ a + 12d = 4a + 8d

4d = 3a
⇒ a =4d/3
t5 = 16
⇒ a + 4d = 16

`⇒((4d)/3)+ 4d = 16`

`(4d+12d)/3=16`

`(16d)/3=16`

d=3

`a=(4d)/3=(4(3))/3=4`

`S_n=n/2[2a+(n-1)d]`

`S_10=10/2[2xx4+(10-1)xx3]`

=5[8+27]

=5x35

=175

Sum of the first 10 terms =175.