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Question
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
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Solution
In the given problem, we need to find the sum of the n terms of the given A.P. 5, 2, −1, −4, −7, ...,
So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2 [2a + (n -1)d]`
Where; a = first term for the given A.P.
d = common difference of the given A.P.
n = number of terms
For the given A.P. (5, 2, -1, -4, -7)
Common difference of the A.P. (d) =`a_2 - a_1`
= 2 - 5
= -3
Number of terms (n) = n
First term for the given A.P. (a) = 5
So, using the formula we get,
`S_n = n/2 [2(5) + (n -1)(-3)]`
`= n/2 [10 + (-3n + 3)]`
`= n/2 [10 - 3n + 3]`
`= n/2 [13 - 3n]`
Therefore, the sum of first n terms for the given A.P. is `n/2 [13 - 3n]`
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