Question

What will be the sum of all the even numbers from 41 to 80?
1. 2080
2. 640
3. 1640
4. 1220

Answer 1

Correct Answer - Option 4 : 1220

Given

Numbers from 41 to 80

All number between 41 to 80 should be even number

Formula used

T_n = a + (n-1)d

S_n = \(\frac{n}{2}\left\{ {2A + \left( {N - 1} \right)D} \right\}\)

Where, T_n = last number in the series

S_n = Sum of series of AP

N = number of terms in series

A = first number of the series

D = difference of consecutive series

Calculation:

Even number between 41 to 80

⇒ 42, 44, 46, 48, 50 ..............80

⇒ This series is in AP

Where, a = 42

⇒ d = a₂ - a₁

_⇒ 44 - 42 = 2

T_n = a + (n-1)d

⇒ 80 = 42 + (n-1)2

⇒ 38 = (n-1)2

⇒ n = 20

⇒ S_n  = \(\frac{{20}}{2}\left\{ {2 × 42 + \left( {20 - 1} \right)2} \right\}\)

⇒ 20{42 + 19}

⇒ 20 × 61

∴ 1220