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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

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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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