Question

Find the sum of all entries of the geometric sequences given below. a) [Geometric Sequence A]

b) [Geometric Sequence B] c) G= { 5/3, 5/9. 5/27, 5/81, ..........5/4782969} d) h= { 1/3, 1/9. 1/27, 1/81, ..........} Please calculate the sum of all entries for each of these geometric sequences.

Answer 1

To find the sum of all entries in a geometric sequence, we can use the formula for the sum of an infinite geometric series. However, for Geometric Sequence A and Geometric Sequence B, we don't have enough information to calculate the sum. For G = {5/3, 5/9, 5/27, 5/81, ...}, the sum is 5/2. For h = {1/3, 1/9, 1/27, 1/81, ...}, the sum is 1/2.

Step-by-step explanation:

To find the sum of all entries in a geometric sequence, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term of the sequence and r is the common ratio.

a) For Geometric Sequence A, we don't have enough information to calculate the sum as we don't know the first term or the common ratio.

b) For Geometric Sequence B, we also don't have enough information to calculate the sum as we don't know the common ratio.

c) For G = {5/3, 5/9, 5/27, 5/81, ...}, the first term a = 5/3 and the common ratio r = 1/3. Plugging these values into the formula, we get S = (5/3) / (1 - 1/3) = 5/2.

d) For h = {1/3, 1/9, 1/27, 1/81, ...}, the first term a = 1/3 and the common ratio r = 1/3. Plugging these values into the formula, we get S = (1/3) / (1 - 1/3) = 1/2.