Question

What is the 100th term of the arithmetic sequence? 3, 8, 13, 18, …

a. 300
b. 498
c. 500
d. 497

Answer 1

The answer is B. 498

An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).
The equation for an arithmetic sequence is

`A_(n) =A_(1) + (n-1)d`

`A_(n)` is the "n-th" number in the sequence (ex:
`A_(1)` is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 3 so
`A_(1) =3`
8-3=5 , 13-8=5 , and 18-13=5 so d=5 (add 5 to get the next number)


`A_(n)=A_(1)+(n-1)d`

`A_(100)=3+(100-1)(5)`

`A_(100)=3+(99)(5)`

`A_(100)=3+495`

`A_(100)=498`

The answer is B. 498

Answer 2

first work out the nth term then the 100th term:

the difference between the numbers is: 5
and that zero term is: -2

so the nth term is: 5n - 2

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now using the nth term we replace n with 100,
then we get: 498

the answer is the above in bold
hope it helped :)