sum of the first n integers

Question

Use the formula for the sum of the first n integers, to evaluate the following:
a) 3 + 6 + 9 + 12 + 15 + 18 + …. + 303
b) 6 + 7 + 8 + 9 + 10 + 11 + …. + 102

Answer 1

an = a1+(n-1)d ... where an is the nth term, a1 is the first term, n is the number of terms, and d is the difference between terms in the sequence.

 

Sum (n) = n*(a1+an)/2

 

so ...

 

a) 303 = 3 + (n-1)(3) ... 303 = 3+3n-3 ... 3n = 303 ... n = 101 ... sum = 101*(3+303)/2 = 15453

 

b) 102 = 6+(n-1)(1) ... 102=6n-6 ... 6n = 108 ... n = 18 ... sum = 18*(6+102)/2 = 972