Question

Create a sequence with five terms based on the given information. a. A arithmetic sequence with a third term of 8 and a constant difference of 5 b. A geometric sequence with a fifth term of 1/3 and constant ratio of 1/3

Answer 1

Part a .

A arithmetic sequence with a third term of 8 and a common difference of 5 .

To find the first five therms, since the common difference is 5, so we add 5 to get the fourth term and add 5 to fourth term to get the fifth term .

And for first two terms, we will subtract 5 from 8 to get the second term and subtract 5 from the second term to get the first term. And we will get

$8-5-5,8-5,8, 8+5+5 = -2 ,3,8,13,18$

Part b:A geometric sequence with a fifth term of 1/3 and constant ratio of 1/3.

TO find the first five terms, since the constant ratio of 1/3, so we multiply 1/3 to third term to get fourth term, and multiply fourth term by 1/3 to get fifth term .

And to get the first two terms, we will divide third term by 1/3, to get the second term and divide the second term by 1/3 to get the first term, that is

$3,1,\frac{1}{3}, \frac{1}{9},\frac{1}{27}$