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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 =
= 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
=
.
It gives at n= 15
=
= 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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