Question

What is the sum of the geometric sequence 4, 16, 64, ƒ if there are 8 terms?

Answer 1

65,535

Explanation:

4 times 4 times 4 times...... count the times you do it till 8. if that's confusing think of this as 4 to the 8th power.

Answer 2

In a Geometric Sequence, each term is found by multiplying the previous term by a constant. For this case, the constant is 4. To find the sum of the geometric sequence with 8 terms, we use the formula as follows:

∑(ar^k) = a ( 1-r^n) / (1-r)

where a is the first term, r is the constant, n is the number of terms

∑(ar^k) = 4 ( 1-4^8) / (1-4)
∑(ar^k) = 87380