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Question
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
Solution
Here, we are given an A.P. whose nth term is given by the following expression,
yn = 9 − 5n. 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 the nth term of A.P.
y = 9 - 5(1)
= 9 - 5
= 4
Now, the last term (l) or the nth term is given
`l = a_n = 9 - 5n`
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_15 = (15/2) [(4) + 9 - 5(15)]`
`= (15/2)[13 - 75]`
= (15/2)(-62)
= (15)(-31)
= -465
Therefore, the sum of the 15 terms of the given A.P. is `S_15 = -465`
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