Question

Copy and complete each table.

HELP I CAN’T FIND THE EQUATION FOR N
I realized the output is -5 each, but what’s the equation ;-;;;l

Answer 1

5th term of sequence = -18

nth term of the sequence = -5n + 7

Explanation:

Difference between successive and previous term of the output,

`T_(2)-T_(1)` = -3 - 2

= -5

Similarly,
`T_(3)-T_(2)=-8-(-3)`

= -5

There is a common difference 'd' = (-5)

Therefore, the sequence formed will be an arithmetic sequence.

First term of the sequence 'a' = 2

Explicit formula of an arithmetic sequence,
`T_(n)` = a + (n - 1)d [n = input value]

`T_(n)` = 2 + (n - 1)(-5)

= 2 - 5n + 5

= -5n + 7

5th term of this sequence,

`T_(5)=2+(5-1)(-5)`

= 2 - 20

= -18

Therefore, 5th term of sequence = -18

nth term of the sequence = -5n + 7