Question

The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence. The function represents the sequence.

Answer 1

Answer:

Function representing the sequence will be f(n) = (23 - 3n)

Step-by-step explanation:

The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....

Let n represents the number of term and f(n) the the term in the sequence.

Then we have to find the function that represents the sequence.

As we know explicit formula of an arithmetic sequence is given by

$T_{n}=a+(n-1)d$ Or the function representing the sequence will be

f(n) = a + (n-1)d

where a represents first term of the sequence a = 20

and common difference d = 17-20 = (-3).

Now the function which represents this sequence will be

f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n

Answer 2

Answer: 17 -3n

Explanation:

In the given arithmetic progression 20,17,14,11,8....

first term that is a = 20

common difference that  is d=  a2-a1 = 17-20 = -3

let n is the nth term

$a_{n}$ = a+(n-1)d

substituting the values of first, common,difference and n

$a_{n}$ =20+(n-1) (-3)

                        = 20 -3n+3

                         =23 -3n

Answer 3

A) f(n) = -3n + 23