What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms?

Solution:

The formula to find the sum of geometric sequence is

a(rⁿ - 1)/ (r - 1)

Where a is the first number

and r is the common ratio

n is the number of terms

It is given that

a = 1

r = 3/1 = 3

n = 10

Substituting it in the formula:

Sum of the geometric sequence = a(rⁿ - 1)/ (r - 1)

= 1 (3¹⁰ - 1)/ (3 - 1)

By further calculation, we get

= 1 (59049 - 1)/ 2

= 59048/ 2

So we get

= 29524

Therefore, the sum of the geometric sequence is 29524.

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What is the sum of the geometric sequence 1, 3, 9, ... if there are 10 terms?

Summary:

The sum of the geometric sequence 1, 3, 9, ... if there are 10 terms is 29524.