Question

PLEASEHELP!!!!!!!!!!

Write an expression to describe a rule of the sequence. Then find the 100th term in the sequence.
4, 9, 14, 19, 24, 29.....
A)4+5n;504
B)5n-1; 499
C) 5n; 500
D) 4n+5; 405

Answer 1

A) 4+5n;504 Would be ur answer!!

Hope i helped:P

Answer 2

Option B is correct

`a_n = 5n-1`; 499

Explanation:

The nth term for the 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 successive terms

n is the number of terms.

As per the statement:

4, 9, 14, 19, 24, 29.....

This is a arithmetic sequence.

Here,
`a_1=4` and d =5

Since,

9-4 = 5,

14-9 =5,

19-14 = 5 and son on....

Substitute the given values in [1] we have;

`a_n = 4+(n-1)5`

⇒
`a_n = 4+5n-5 = 5n-1`

⇒
`a_n = 5n-1`

We have to find the 100th term in the given sequence.

For n= 100

`a_(100) = 5(100)-1=500-1 =499`

⇒
`a_(100) = 499`

Therefore, an expression to describe a rule of the sequence is,
`a_n = 5n-1` and the 100th term in the sequence is 499