The graph shows the first three terms in a geometric sequenc

The graph shows the first three terms in a geometric sequence. What is the common ratio r? Explain or show how you determined your answer. What is the recursive formula for the sequence? What is the iterative formula for the sequence? Show how to use your answer from Part (c) to find the eighth term of the sequence.

Solution

( 1, 2) , ( 2,5 ) , ( 3, 12.5)

first term a1 = 2 ,

second term = 5

third term = 12.5

common ratio is next term / previous term = 5/2 = 2.5

b) recursive formula for geometric sequence is given by

An = r*( A n-1 )

An = 2.5 ( A n-1 )

c) iterative formula is igiven by

An = a1 * r ^(n-1)

An = 2 (2.5)^n-1

d) 8th term of the sequence is plug n = 8

A8 = 2 (2.5)^7

a8 = 1220.7031