Question

Sum of 1-100th term in AP

Answer 1

AP = 1 , 2 , 3 , 4........., 100



Here,


First term ( a ) = 1


Common difference ( d ) = 2 - 1 = 1


Last term ( Tn ) = 100



a + ( n - 1 ) × d = 100


1 + ( n - 1 ) × 1 = 100



1 + n - 1 = 100


n = 100


Number of terms = 100



Sn = n/2 × [ 2a + ( n - 1 ) × d ]




S100 = 100/2 × [ 2 × 1 + ( 100 - 1 ) × 1 ]




=> 50 ( 2 + 99 )



=> 50 × 101


=> 5050



Hence,

Sum of the terms of the given AP Will be equal to 5050.