Answer:
The fifth term of the sequence is 16
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 =