Use the arithmetic sum formula to find out the value for thi

Use the arithmetic sum formula to find out the value for this: 1+2+3+4+5++101

1. Use the arithmetic sum formula to find out the value for this: 1+2+3+4+5+.. 101

The given series 1 + 2 + 3 + 4 + 5 +...............+101 is an arthmetic series,

Where first term (a) = 1, common difference = 1, and n(number of terms) = 101

So, using the arithmetic sum formula,

S= (n/2)(2a + (n - 1) d)

= (101/2)( 2 x 1 + ( 101 - 1 ) x 1)

= ( 101 /2) ( 2 + 100)

= ( 101/2) x 102

= 101 x 51

= 5,151

Therefore, the value of 1 + 2 + 3 + 4 + 5 +...............+101is 5,151.

Note: We can also use the arithmetic sum formula,S= (n/2)(a + l), here l is the last term.