Question

Part1; The nth term of a geometric sequence is given by a_n = 4(0.75)^n-1, write the first five terms, and find the 5th partial sum. (20 points)

Part2; The nth term of an arithmetic sequence is given by a_n=3n+2, write the first 4 terms and find the 8th partial sum.

Explain your answers!


First five terms:
5th partial sum:

First 4 terms:
8th partial sum:

Answer 1

Just take n=1,2,3,4,5 respectively to find out the first 5 terms.

First 5 terms = 4,3,2.25,1.69 respectively.

For the 5th partial sum, just add the first 5 terms.

5th partial sum = 10.34

....

First 4 terms : 5,8,11,14 respectively.

Now you need to find the other next 4 terms to find out the 8th partial sum.

17,20,23,26

8th partial sum = 124

Hope this helps:)