Question

What will come in place of question mark (?) in the following question?

1² – 2² + 3² – 4² + 5² – ………….. – 14² = ?

1. -100
2. -105
3. -110
4. -108
5. -102

Answer 1

Correct Answer - Option 2 : -105

Given:

1² – 2² + 3² – 4² + 5² – ………….. – 14²

Formula used:

a² – b² = (a + b)(a – b)

Calculation:

1² – 2² + 3² – 4² + …………….. – 14²

⇒ [(1² – 2²) + (3² – 4²) + ………………………… + (13² – 14²)]

⇒ [(1 – 2)(1 + 2) + (3 – 4)(3 + 4) + ………………………. + (13 – 14)(13 + 14)]

⇒ [(-1)(3) + (-1)(7) + ……………………. + (-1)(17)]

⇒ (– 3 – 7 – 11 – 15 – 19 – 23 – 27)

⇒ –105

∴ The value of ‘?’ is –105.