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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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