The sum of the first 10 terms of a geometric sequence is 1023. The common ratio is 2. What is the fifth term of the sequence?

The fifth term of the sequence is 16

Step-by-step explanation:

Firstly, we need to write the mathematical expression for the sum of terms in a geometric sequence.

Mathematically, the sum of terms S is calculated as follows;

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

where a is the first term of the sequence, r is the common ratio, and n is the number of terms. From the question, we can see we have 10 as the number of terms here, 1023 as the sum, and 2 as the common ratio. We thus, plug these values into the equation above.

1023 = a (2^10 - 1) / 2-1

1023 = a (1024-1) / 1

1023 = 1023a

a = 1023/1023

a = 1

In the question we are told to find the fifth term:

mathematically, the nth term of a geometric sequence can be calculated using the formula Tn = ar^ (n-1). For the fifth term, n = 5 and thus T5 = ar^4

T5 = 1 * 2^4 = 1 * 16 = 16

T5 =