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  • How many terms of the AP: -15, -13, -11, _______ are needed to make the sum -55? Explain the reason for double answer.

How many terms of the AP: -15, -13, -11, _______ are needed to make the sum -55? Explain the reason for double answer.

Answers (1)

Here the given AP is -15, -13, -11$ \ldots $ \\

 First term (a) = - 15 

 Common difference (d) = - 13 - (-15) = - 13 + 15 = 2 

 Let n terms have sum - 55 then 

{{S}_{n}}=-55

{{S}_{n}} =\frac{n}{2}\left[ 2a+\left( n-1 \right)d \right]

n[-30 + 2n - 2] = -55 \times 2 \\ -32n + 2n^2 + 110 = 0 \\ 2n^2 - 32n + 110 = 0 \\ n^2 - 16n + 55 = 0 \\ n^2 - 5n - 11n + 55 = 0 \\ n(n - 5) - 11(n - 5) = 0 \\ (n - 5)(n - 11) = 0 \\ n = 5, 11

There are two answers which are 5th when n=5 all terms are negative and 11th terms when n=11  the AP will contain positive numbers and negative terms so the resulting sum is - 55.  

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infoexpert21

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