Question

How many terms of the progression 3,6,9,12....must be taken at the least to have a sum not less than 2000?​

Answer 1

You need at least 37 terms to have a sum of 2000 or more

Explanation:

,

S(n):=3+6+9+12+⋯+3n=3⋅n(n+1)2

This is approximately 32⋅n2.

It should be around 2000, that is n2 should be around 2/3⋅2000≈1334. Using calculator, its square root is ≈36.52 and if you sustitue n=36 to S(n) gives S(36)=1998.

So since 36 is not enough you need 37 terms to have a sum of 2000 or more