Question

Find a9 in the arithmetic sequence with a1 = -2.75 and d = 0.25

Answer 1

The ninth term is -0.75.

Explanation:

Let's write the actual formula for this arith. seq.

It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.

Here, a(n) = -2.75 + (n - 1)(0.25)

So the ninth term of this sequence is

a(9) = -2.75 + (9 - 1)(0.25

= -2.75 + 8(0.25)

= -2.75 + 2

= -0.75

The ninth term is -0.75.

Answer 2

`a_9=-0.75`

Explanation:

The given sequence has the first term,
`a_1=-2.75` and d=0.25

The general formula for an arithmetic sequence is given by;

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

Since we want to find
`a_9`, it means n=9

We substitute the given values into the formula to obtain;

`a_9=-2.75+0.25(9-1)`

`a_9=-2.75+0.25(8)=-0.75`

Hence, the 9th term is

`a_9=-0.75`