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Question
The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 then the sum of its first ten terms is ______.
Options
150
175
160
135
MCQ
Fill in the Blanks
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Solution
The 13th term of an AP is 4 times its 3rd term. If its 5th term is 16 then the sum of its first ten terms is 175.
Explanation:
T13 = 4 × T3
⇒ a + 12d = 4(a + 2d)
⇒ 3a – 4d = 0
T5 = 16
⇒ a + 4d = 16
On solving (i) and (ii), we get a = 4 and d = 3
`S_10 = 10/2 (2a + 9d)`
= 5(2 × 4 + 9 × 3)
= 175
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