Find S25 for -7 + -2 + 3 + 8 + ....  Please show your work.Al

Luca B. | Certified Educator

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You should notice that the terms of the sum represent the terms of algebraic progression with common difference `d=5` .

You may evaluate the sum of 25 terms such that:

`S_25 = ((a_1+a_25)*25)/2`

You may evaluate `a_25`  using the following formula such that:

`a_25 = a_1 + 24*d => a_25 = -7 + 24*5 => a_25 =113`

`S_25 = ((-7+113)25)/2 => S_25 = 53*25 => S_25 = 1325`

Hence, evaluating the usm of 25 terms yields `S_25 = 1325` .

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