Nicholas found the 13th term of the geometric sequence 15, 30, 60, 120 the following way: A(13) = 15 * 213
A(13) = 15 * 8,192
A(13) = 122,880

Is Nicolas correct? Why or why not? (Make sure to justify your answer) If Nicolas is incorrect please state the correct solution.

No. Nicolas is wrong.

Step-by-step explanation:

The formula for calculating nth term of a geometric sequence is given as:

= ar^n-1.

where a = first term = 15

r = common ratio = 30/15 = 2

n = 13

Using the formula,

= ar^n-1

= 15 × 2^(13-1)

= 15 × 2^12

= 15 × 4096

= 61440

The 13th term is 61440. Nicolas is wrong.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.