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Question
What is the sum of first n terms of the AP a, 3a, 5a, …..
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Solution
The given AP is 3a,5a,........
Here,
First term, A = a
Common difference, D = 3a - a = 2a
∴ Sum of the n terms, n S
`= n/2 [2xx a+ (n-1) xx 2a] { s_n = n/2 [ 2A +(n-1) D]}`
`= n/2 (2a + 2an -2a )`
`= n/2 xx 2 an`
= an2
Hence, the required sum is an2 .
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