Question

Find the 97th term of the arithmetic sequence 17, 26, 35, ...

Answer 1

881

Explanation:

Arithmetic sequences can be written as:

`a_n = a_1 + (n-1)d\\a_1 \: is \: 17\\a_n = 17 + (n-1)d\\`

The second term is 26,

`26 = 17 + (2-1)d\\9 = 1d\\d = 9\\a_n = 17 + (n-1)*9\\a_n = 17 + 9n - 9\\a_n = 8 + 9n`

So, the
`97^t^h` term is

`a_9_7 = 8 + 9(97)\\a_9_7 = 8 + 873\\a_9_7 = 881`