The sum 12 - 22 + 32 - 42 + 52 - 62 + ... - 202 is equal to ?
Answers
(-10)+(-10)+........10 times
=-100
The sum of 12 - 22 + 32 - 42 + 52 - 62 + ... - 202 is equal to -100.
We have to find the sum of 12 - 22 + 32 - 42 + 52 - 62 + .... -202.
There are two series in the given series.
First one is ; 12 + 32 + 52 + ...
2nd one is ; -22 - 42 - 62 -... -202
From 2nd one,
- first term, a = -22
- common difference, d = -20
- last term, aₙ = -202
Using formula, aₙ = a + (n - 1)d
⇒ -202 = -22 + (n - 1) × -20
⇒ -180/-20 = n - 1
⇒ n = 10
Now, 10th term of first one,
⇒ a₁₀ = 12 + (10 - 1) × 20 = 12 + 9 × 20 = 192
Hence, the series can be written as ; 12 - 22 + 32 - 42 + 52 - 62 + .... + 192 - 202
= (12 - 22) + (32 - 42) + (52 - 62) + .... upto 10th term {i.e., {192 - 202}
= (-10) + (-10) + (-10) + ... upto 10th terms
= 10 × -10
= -100
Therefore the sum of 12 - 22 + 32 - 42 + 52 - 62 + ... - 202 is equal to -100.
Also read similar questions : given that (12+22+32+.......102)=385 ,then the value of (22+42+62+.......+202) is
https://brainly.in/question/3053452
The sum of the 20th term of the series 12+22+32+42+52+62 is
https://brainly.in/question/7977433
#SPJ3