Question

The sum of all even numbers between 5 and 100 is

1 point

2400

2442

2444

2542

​

Answer 1

Given :-

• A.P = 6 , 8 , 10 ......., 98

• First term = 6

• Common difference = 2

• Last term = 98

To Find :-

• Sum of even numbers between 5 and 100

Solution :-

Firstly we have to find number of terms

$\large \implies \underline{\boxed{\sf A_n = a + (n - 1)d}} \\ \\ \implies \sf98 = 6 + (n - 1)2 \\ \\ \implies \sf 98 - 6 = (n - 1)2 \\ \\ \implies \sf92= (n - 1)2 \\ \\\implies \sf n -1 = \frac{92}{2} \\ \\ \implies \sf n = 46 + 1 \\ \\ \implies \sf n = 47$

Now , sum of these terms is

$\large\implies\underline{ \boxed{ \sf S_n = \frac{n}{2} \big( a + l \big)}} \\ \\ \implies \sf S_n = \frac{47}{2} (6 + 98) \\ \\ \implies \sf S_n = \frac{47}{2} \times 104 \\ \\ \implies \sf S_n = 47 \times 52 \\ \\ \implies \underline{\boxed{ \sf S_n = 2444} }$