SOLUTION: Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.

Algebra ->  Sequences-and-series -> SOLUTION: Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.      Log On


   



Question 1202439: Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.
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The sequense  -396, -308, -220, -132, . . ., 836  is an arithmetic progression
with the first term  a= -396  and the common difference of d= 88  
(sinse -308 - (-396) = 88  and each next term is 88 units greater than the current term).


Find the number of term. Use the formula for the n-th term

    836 = -396 + 88*(n-1).


It gives  (836 + 396) = 88*(n-1);  n-1 = %28836%2B396%29%2F88 = 14;  hence,  n= 15.

CHECK.  -396 + (15-1)*88 = use your calculator = 836,  correct.


To find the sum of this AP, use the general formula for the sum of an AP

    S%5Bn%5D = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An.


It gives at n= 15

    S%5B15%5D = %28%28-396%2B836%29%2F2%29%2A15 = use your calculator = 3300.   ANSWER

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.


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