Please Help?

Question

2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:

a) What is r, the ratio between 2 consecutive terms?

b) Using the formula for the nth term of a geometric sequence, what is the 24th term?

c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?


3) Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:

a) What is r, the ratio between 2 consecutive terms?

b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.

d) What observation can make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?

Answer 1

2a) r = 2
2b) a[24] = 1•2^23 = 2^23
2c) S[10] = 1[1-2^10]/[1-2] = 2^10 - 1 = 1023

3a) r = 1/2
3b) S[10] = 1[1-(1/2)^10]/[1-1/2] = 1.9980 ... actually 2 - 1/512
3c) S[12] = 1[1-(1/2)^12]/[1-1/2] = 1.9995 ... actually 2 - 1/2048
3d) sum just under 2. limit [n→∞] = 2