Question

Find the 7th term in the following sequence: `1, 4, 7, 10, cdots`?

Answer 1

`color(green)(19)`

Explanation:

The sequence appears to be an arithmetic sequence with a difference between terms of `color(blue)(3)`.

In general given a first term: `color(red)(a_1)`
and a difference between successive terms: `a_n-a_(n-1)=color(blue)(d)`

the `n`th term can be calculated as `a_n=color(red)(a_0)+color(blue)(d) * (n-1)`

Therefore the `7`th term of the given sequence should be
`color(white)("XXX")a_7=color(red)(1)+color(blue)(3) * (7-1) = 19`