What is the sum of the first 21 terms of the series 1 - 5 + 4 - 9 + 7 - 13 + 10 - 17 + ....
Answers
Given : 1-5+4-9+7-13+10-17 + ...
To Find : sum of the first 21 terms
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
Sum of Arithmetic sequence (AP) is called Arithmetic series
1-5+4-9+7-13+10-17 + ...
Break the series in 2 part
1 + 4 + 7 + 10 + ...
-(5 + 9 + 13 + ...)
1st series has 11 terms and second series has 10 terms in 21 terms
1 + 4 + 7 + 10 + ...
n = 11 , a = 1 , d = 3
Sₙ = (n/2)(2a + (n - 1)d)
= (11/2)(2 + 10(3))
= 11 * 16
= 176
5 + 9 + 13 + ...
n = 10 , a = 5 , d = 4
Sum = (10/2)(10 + 9*4)
= 5(46)
= 230
176 - 230 = -54
Hence sum of the first 21 terms is -54
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