#### 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.

#### Solution

Let the first term be ‘a’ and the common difference be ‘d’ of the A.P.

t_{13} = 4t_{3}

⇒ 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.

Is there an error in this question or solution?

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