Question

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

Answer 1

Answer:

$A(1)=9$

$A(2)=4$

$A(3)=-1$

Arithmetic sequence

Step-by-step 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.