Question 1 Write a conjecture that describes the pattern in the sequence, and then use the conjecture to find the next term in the sequence.
2,8, 32, 128,...
100 words remaining

T5 = 512

Step-by-step explanation:

Given the sequence

2,8, 32, 128,...

The sequence is a geometric progression

nth term of a geometric progression is expressed as:

Tn = ar^n-1

a is the first term = 2

n is the number of terms = 5 (next term is the 5th term)

r is the common ratio = 8/2 = 32/8 = 4

Substitute and get the fifth term

T5 = 2(4)^5-1

T5 = 2(4)^4

T5 = 2*256

T5 = 512

Hence the next term is 512