Question

1. ) 14, 11, 8, 5, ... a. Identify each sequence as arithmetic or geometric, explain your answer. b. Find the next five terms. c. Write an explicit formula for the sequence. d. Write a recursive formula for the sequence. 2.) 2, 10, 50, 250, ... a. Identify each sequence as arithmetic or geometric, explain your answer. b. Find the next five terms. c. Write an explicit formula for the sequence. d. Write a recursive formula for the sequence.

Answer 1

The terms of the sequence are 14, 11, 8, 5, .....

Since

11 - 14 = -3

8 - 11 = -3

5 - 8 = -3

there is a constant difference between each two consecutive terms

then the sequence is an arithmetic sequence

The next five terms are

5 + -3 = 2

2 + -3 = -1

-1 + -3 = -4

-4 + -3 = -7

-7 + -3 = -10

The next five terms are

2, -1, -4, -7, -10

The explicit formula is

$an=a+(n-1)d$

an is any term in the sequence

a is the first term

d is the constant difference

n is the position of the number

a = 14

d = -3

$an=14+(n-1)(-3)$

Multiply -3 by the bracket

an = 14 + (-3)(n) - (-3)(1)

an = 14 - 3n + 3

Add the like terms

an = 17 - 3n

The explicit formula is an = 17 - 3n

The recursive formula is

First-term = 14, an = an-1 + d

First term = 14; an = an-1 + (-3)

$a_1=14;a_n=a_{n-1}+(-3)$