Question

The sequence is recursive. Find the value of the next term in the sequence 7, 1, -5, -11, -17,

Answer 1

There is no "standard" way to solve an exercise like this: you just have to eyeball the sequence and try to find/guess the pattern.

The most common (and easy!) examples are arithmetic or geometric sequence, where the difference or ratio between two consecutive terms is constant.

This is one of those cases: this is an arithmetic sequence, because you obtain every next term by subtracting 6 from the previous one:

`a_1 = 7\\a_2 = a_1-6 = 7-6 = 1\\a_3 = a_2-6 = 1-6 = -5\\a_4 = a_3-6 = -5-6 = -11\\a_5 = a_4-6 = -11-6 = -17`

So, we can deduce

`a_6 = a_5-6 = -17-6 = -23`

Answer 2

-23

Explanation:

Each term is 6 less than the past term. Hopw this helps!