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Question

Find the sum of first 17 terms of an AP whose 4th and 9th terms are 15 and 30 respectively.

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Solution

Let a and d be the first term and the common difference of the given AP respectively. Then,
a4=15a+3d=15 ...(1)
a9=30a+8d=30 ...(2)
On subtracting (2) from (1), we get
5d=15d=3
Putting d=3 in (1), we get
a=153×3=6
Now, Required sum=S17=172[2×6+(171)×3]
S17=172[60]=510

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