Question

Urgent please help!! What is the 100th number in the arithmetic sequence 1, 9, 17, 25, ...?

Answer 1

The 100th term is 793.

Explanation:

Notice that this arithmetic sequence has first term
`a_1=1`

and common difference
`d=8` (since each consecutive term is built by adding "8" to the previous one)

Recall the general formula for the nth term of a sequence:

`a_n=a_1\,+(n-1)\,d`

therefore, for our articular case, the term 100th can be obtained with:

`a_n=a_1\,+(n-1)\,d\\a_(100)=1\,+(100-1)\,8\\a_(100)=1\,+(99)\,8\\a_(100)=1\,+792\\a_(100)=793`

Answer 2

Answer: 793

Explanation:

1 + 8 = 9

9 + 8 = 17

17 + 8 = 25

If 25 is the fourth term in the sequence, and the formula is + 8 for every term, then you need to find 96 more terms with + 8.

96 * 8 = 768

768 + 25 = 793