Question

Find an explicit formula for the arithmetic sequence − 45 , − 30 , − 15 , 0 , . . . −45,−30,−15,0,...minus, 45, comma, minus, 30, comma, minus, 15, comma, 0, comma, point, point, point.

Answer 1

The explicit formula for given sequence is:

a_n=-60+15n

Step-by-step explanation:

Given sequence is:

− 45 , − 30 , − 15 , 0, ......

The general explicit formula for arithmetic sequence is given by

$a_n=a_1+(n-1)d\\Here,\\a_n\ is\ the\ nth\ term\\a_1\ is\ the\ first\ term\\d\ is\ the\ common\ difference$

In the given sequence

$a_1=-45\\a_2=-30\\a_3=-15\\d=a_2-a_1 = -30-(-45) = -30+45 = 15\\a_3-a_2 = -15-(-30)=-15+30=15$

So,

d=15

Putting the value of a1 and d in equation

$a_n=-45+(n-1)(15)\\a_n=-45+15n-15\\a_n=-60+15n$

Hence,

The explicit formula for given sequence is:

a_n=-60+15n

Keywords: Arithmetic sequence, Common difference

Learn more about arithmetic sequence at:

• brainly.com/question/2821386
• brainly.com/question/2860697

#LearnwithBrainly

Answer 2

Answer:

-45+15(n-1)

Step-by-step explanation: