find the sum of 20terms of series 2-4+6-8+10-12+.....
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Answered by
1
answer is 420 2+4+.......38+40= 420
Answered by
2
Answer:
- 20
Step-by-step explanation:
Method 1:
Series is 2-4+6-8+10-12+14-16+.....
= (2-4) + (6-8) + (10 - 12) + (14-16) + .....
Sₙ = n/2(2a + (n-1)d)
a = 2-4, d = (6-8) - (2-4) = 0, n = 10 (since 20 terms = 10 pairs of 2 each)
S = 10/2[2(2-4) + (10-1)0] = 10/2 * - 4 = -20.
Method 2:
2-4+6-8+10-12+14-16+....
Split the series into two different series which will be of 10 terms each and then find the sum of each individual series and add them up as shown below.
= (2 + 6 + 10 + 14 +.... 10 terms) - (4 + 8 + 12 + 16....10 terms)
We know that Sₙ = n/2(2a + (n-1)d)
= [10/2(2*2+ (10-1)4)] - [10/2(2*4+ (10-1)4)]
= [5*40] - [5*44]
= 200 - 220 = - 20.
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