Question

Example 2 Determine the sum of the first 100 terms for the series 2+5+ 8 + ...​

Answer 1

S₁₀₀ = 15050

Explanation:

There is a common difference between consecutive terms

5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 3 , then

S₁₀₀ =
`(100)/(2)` [ (2 × 2) + (99 × 3) ]

= 50 (4 + 297)

= 50 × 301

= 15050

Answer 2

15050

Explanation:

Hello!

So basically, this arithmetic sequence follows the rule (3n-1). What you are looking for is the summation of (3n-1) with a lower limit of 1 and an upper limit of 100. This, plugging it into a calculator (etc. symbolab) or even calculating it manually, we get ∑↑100↓n=1⇒3n-1=15050.