the first term of a geometeic series is 1, the common ratio is 2, and the sum of the series is 63. How many terms are there in this geonetric series?

6 terms

Step-by-step explanation:

To find the number of terms we will use the formula:

Sn = a (1-r^n) / 1-r

where a is the first term = 1

r is the common ratio = 2

Sn is the sum of series = 63

n is the number of terms = ?

Now substitute the values in the formula:

Sn = a (1-r^n) / 1-r

63 = 1 (1-2^n) / 1-2

63=1 (1-2^n) / -1

63*-1 = 1 (1-2^n)

-63 = 1-2^n

Now combine the constants:

-63-1 = - 2^n

-64 = - 2^n

64 = 2^n

2^6 = 2^n

When the base are same powers are equal to each other.

6=n

Thus there are 6 terms ...