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प्रश्न
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
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उत्तर
Here, we are given an A.P. whose nth term is given by the following expression
We need bn = 5 + 2n 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 = 1inthe given equation for the nth term of A.P
b = 5 + 2(1)
=- 5 + 2
= 7
Now, the last term (l) or the nth term is given
`l = b_n = 5 + 2n`
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) + 5 + 2(15)]`
`=(15/2)[12 + 30]`
`= (15/2)(42)`
= (15)(21)
= 315
Therefore, the sum of the 15 terms of the given A.P. is `S_15 = 315`
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