Question

Question 18
Look at this sequence.

95, 80, 65, 50, ...
Which function represents this sequence?

A
a(n)=−15n+110

B
a(n)=110n−15

C
a(n)=95n−15

D
a(n)=−15n+95

Answer 1

Answer:

The function which represents this sequence will be:

$a_n=-15n+110$

Hence, option (A) is true.

Step-by-step explanation:

Given the sequence

$95, 80, 65, 50, ...$

An arithmetic sequence has a constant difference 'd' and is defined by  

$a_n=a_1+\left(n-1\right)d$

computing the differences of all the adjacent terms

$80-95=-15,\:\quad \:65-80=-15,\:\quad \:50-65=-15$

As the difference is the same, so

$d = -15$

as

$a_1=95$

Thus, substituting $d = -15$, $a_1=95$ in the nth term of an arithmetic sequence

$a_n=a_1+\left(n-1\right)d$

$a_n=-15\left(n-1\right)+95$

$a_n=-15n+110$

Therefore, the function which represents this sequence will be:

$a_n=-15n+110$

Hence, option (A) is true.