Question

Write the first three terms in the following sequences. Identify them as arithmetic or geometric

a. A(n + 1) = A(n) − 5 for n ≥ 1 and A(1) = 9

Answer 1

`A(1)=9`

`A(2)=4`

`A(3)=-1`

Arithmetic sequence

Explanation:

We are given that

`A(n+1)=A(n)-5 \;for\;n\geq 1` A(1)=9

We have to find first three terms and identify the sequence is geometric or arithmetic.

Substitute n=1

Then, we get

`A(2)=A(1)-5=9-5=4`

For n=2

`A(3)=A(2)-5=4-5=-1`

For n=3

`A(4)=-1-5=-6`

`d_1=A_2-A_1=4-9=-5`

`d_2=A_3-A_2=-1-4=-5`

`d_3=A_4-A_3=-6+1=-5`

`d_1=d_2=d_3=-5`

When the difference of consecutive terms are constant then the sequence is arithmetic sequence.

Therefore, given sequence is arithmetic sequence.