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If I understand your sequence, then this is the "closed form" of the sequence:
a_n = 63 - 4 n
Sum = (59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3) = 465
Sum of the series 900-841+784+...+36-25+16-9+4-1 = 465.
A series is a set of numbers following some specific pattern.
An Arithmetic Progression (known as A.P.), is a special series where every term is the sum of the previous term and a constant(d), with the first term also being a constant(a).
We are given a series:
900 - 841 + 784 - ......... + 36 - 25 + 16 - 9 + 4 -1.
Taking two numbers at a time in this series, we get:
59, 55, 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3.
The above series is an Arithmetic Progression, with first term a=3, the constant difference(d) = 4, the last term(l) = 59, and the number of terms(n) = 15
To find its sum, we use the formula of the sum of an Arithmetic Progression for first n numbers,
Sₙ = {(a+l)*n}/2
∴ Sum of the series = {(3+59)*15}/2 = (62*15)/2 = 31*15 = 465.
∴ Sum of the series 900-841+784+...+36-25+16-9+4-1 = 465.
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