Question

Write an expression to describe a rule for the sequence. Then find the 100th term in the sequence. 5, 13, 21, 29, 37, 45, … (1 point)

• 8n; 800
• 8n – 3; 797
• 3n – 8; 292
• 5 + 8n; 805

Answer 1

Here, a = 5, d= 13-5 = 8

A(n) = 5+(n-1)8

A(n) = 5+8n-8

A(n) = 8n-3

A(100) = 8(100) - 3 = 800-3 = 797

SO OPTION B IS YOUR ANSWER,....

Answer 2

Option B is correct

8n – 3;

797

Explanation:

The nth term of an arithmetic sequence is given by:

`a_n = a_1+(n-1)d` ....[1]

where

`a_1` is the first term

d is the common difference of two consecutive terms.

n is the number of terms.

Given the sequence:

5, 13, 21, 29, 37, 45, …

This is an arithmetic sequence with first term
`a_1` = 5 and common difference(d) = 8

Since;

13-5 = 8,

21-13 = 8,

29-21 = 8 and so on....

We have to find the 100th term in the sequence

Substitute in [1] we have;

`a_n= a_1+(100-1)d`

⇒
`a_n = 5+(n-1)8 = 5 +8n -8 = 8n -3`

Substitute the given values and n=100 we have;

`a_(100) =800 -3= 797`

Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;