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# 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. - CBSE Class 10 - Mathematics

#### Question

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.

#### Solution

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.

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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.
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