FIND THE SUM OF 20 TERMS OF THE SERIES
12 - 22 + 32 -42 +52 -62 +.....20 TERMS.
Answers
Final answer is -200.
The sum of 20 terms of the given series is -100.
Given:
12 - 22 + 32 -42 +52 -62 +.....20 TERMS.
To Find:
The sum of 20 terms of the given series.
Solution:
We are required to find the sum of 20 terms of the given series.
The sum of n terms in the arithmetic progression is given as
S = n/2[2a + (n − 1) × d] ---------(1)
The given series can be written as
(12 - 22) + (32 -42) + (52 -62) +.....20 TERMS.
On doing the above calculation the 20 terms have been reduced to 10 terms.
-10-10-10-........10 terms
The above series is the arithmetic progression having
a = -10
d = -10-(-10)
d = -10+10
d = 0
n = 10 terms
Substitute the values of a,d, and n in equation(1)
S = 10/2[2×(-10)+(10-1)×0]
S = 5[-20]
S = -100
Therefore, The sum of 20 terms of the given series is -100.
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