Question : What is the value of $98^{2} - 97^{2} + 96^{2} - 95^{2} + 94^{2} - 93^{2} + \dots \dots 12^{2} - 11^{2}$ ?
Option 1: 4725
Option 2: 4796
Option 3: 4851
Option 4: 4926

Question

Question : What is the value of the expression $1 - 7 + 2 - 8 + 3 - 9 + 4 - 10 + \dots \dots$ to 100 terms?

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Answer 1

Correct Answer: 4796

Solution : Given: $98^{2} - 97^{2} + 96^{2} - 95^{2} + 94^{2} - 93^{2} + \dots \dots 12^{2} - 11^{2}$
$= (98 + 97) (98 - 97) + (96 + 95) (96 - 95) + (94 + 93) (94 - 93) . . . . . . . (12 + 11) (12 - 11)$
$= 195 + 191 + 187 + . . . . . . + 23$
Here $a = 195$ , $d = 191 - 195 = - 4$
$T_{n} = a + (n - 1) d$
⇒ $23 = 195 + (n - 1) (- 4)$
⇒ $n - 1 = \frac{23 - 195}{- 4}$
⇒ $n - 1 = \frac{- 172}{- 4}$
⇒ $n - 1 = 43$
⇒ $n = 44$
Sum of the series = $\frac{n}{2} (a_{1} + a_{n})$ , where $n$ is the number of terms, $a_{1}$ is the first term, and $a_{n}$ is the last term.
Here, $n = 44$ (from 195 to 23)
$a_{1} = 195$
$a_{n} = 23$
So, the sum of the series = $\frac{44}{2} (195 + 23) = 22 \times 218 = 4796$
Hence, the correct answer is 4796.

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Question : What is the value of 982−972+962−952+942−932+……122−112?Option 1: 4725Option 2: 4796Option 3: 4851Option 4: 4926

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Question : What is the value of $98^{2} - 97^{2} + 96^{2} - 95^{2} + 94^{2} - 93^{2} + \dots \dots 12^{2} - 11^{2}$ ?
Option 1: 4725
Option 2: 4796
Option 3: 4851
Option 4: 4926