Question

Find the 100-th term of the following sequence

3, 10, 17, 24, …

Also find the sum of the first 100 terms.

Answer 1

Below in bold.

Explanation:

This is an arithmetic sequence with a1 = 3 and d = 7.

So, 100th term

= a1 + d(n - 1)

= 3 + 7(100-1)

= 696.

Sum (100) =

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

= 50(6 + 99*7)

= 50 * 699

= 34950.

Answer 2

696

Explanation:

*nth term = 7n - 4

n = 100

7 × 100 - 4 = 696

So the 100th term of the following sequence is: 696

*To find the nth term:

• They all increase by 7 so it is 7n
• 3 - 7 = -4 so then it is 7n - 4