Question

HELP PLEASE

EXPLAIN THE ANSWER TOO

write the formula for the sequence : 10, 6.5, 3, -0.5, -4…

Answer 1

`a_n = -3.5 (n - 1) + 10`

Explanation:

This sequence is arithmetic in nature because we are subtracting 3.5 to get from one term to the next. Write the general formula for an arithmetic sequence as shown below.

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

...where
`a_1` is the first term of the sequence, d is the difference in terms, n is the term number, and
`a_n` is the nth term.

You find d by subtracting consecutive terms to see a pattern. If you don't want to find d this way, substitute in all other values in the equation and solve for d. I will use 6.5 to find d and it is the second (2nd) term of the sequence; n = 2,
`a_1` = 10,
`a_2 = 6.5`.

6.5 = d(2-1) + 10

d = 6.5 - 10

d = 3.5

So the equation for this sequence is:

`a_n = -3.5 (n - 1) + 10`

Answer 2

x-3.5

Explanation:

`10 - 3.5 = 6.5 \\ 6.5 - 3.5 = 3 \\ 3 - 3.5 = - 0.5 \\ - 0.5 - 3.5 = - 4`

x is whatever last number you got as a result