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An arithmetic series –56 – 44 – 32 – 20 – ... +tₙ  has a sum of 988. Determine the number of terms in the series.

 May 19, 2022
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First term = -56

Common difference = (-44) - (-56) = 12

Let n be the number of terms. Using the formula for arithmetic series,

\(\dfrac n2 (2(-56) + (n - 1)(12)) = 988\)

 

This is now a quadratic equation in n. Can you take it from here? Just note that n is a positive integer.

 May 19, 2022

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