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Question
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
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Solution
Here, we are given an A.P. whose nth term is given by the following expression `a_n = 3 + 4n`. We need to find the sum of first 15 terms.
So, here we can find the sum of the n terms of the given A.P., using the formula,
`S_n = (n/2)(a + l)`
Where a = the first term
l = the last term
So, for the given A.P,
The first term (a) will be calculated using n = 1 in the given equation for nth term of A.P.
a= 3 + 4(1)
= 3 + 4
= 7
Now, the last term (l) or the nth term is given
`l = a_n = 3 +4n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_15 = (15/2) [(7) + 3 + 4 (15)]`
`= (15/2)[10 + 60]`
= (15/2)(70)
`= (15)(35)`
= 525
Therefore, the sum of the 15 terms of the given A.P. is `S_15 = 525`
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