Question

i. What is the sum of first 20 natural numbers? 

ii. The algebraic form of an arithmetic sequence is 6n + 5. 

Find the sum of first 20 terms of this sequence?

Answer 1

i. Sum of first n natural numbers = n(n + 1)/2

∴ Sum of first 20 natural numbers

= 20 x (20 + 1)/2 = (20 x 21)/2

= 420 / 2 = 210

ii. The algebric form = 6n + 5

Common difference 'd' = coefficient of n = 6

First term 'x₁' = (coefficient of n) + (constant term) = 6 + 5 = 11

Sum of first 20 terms

= \(\frac{1}{2}\) an(n + 1) + nb

= \(\frac{1}{2}\) x 6 x 20 x 21 + 20 x 5

= 3 x 20 x 21 + 100

= 1260 + 100 = 1360