How do you find the explicit formula for a geometric sequence 9,19, 39,79,159,...?
Answers
Answer:
Step-by-step explanation:
A geometric sequence is a sequence in which there is a common ratio between successive terms. The sequence is close to a geometric sequence, however. If we add 1 to each term, then the sequence will become as 10. 20. 40.80.160 and so on.This is a geometric sequence with initial term 10 and common ratio 2
Thus,
The difference between 9 and 19 is 10
The difference between 19 and 39 is 20
The difference between 39 and 79 is 40
The difference between 79 and 159 is 80
Thus, the next difference will be =80*2=160
Therefore the next number=160+159= 319
The general term for a geometric series with common ratio r and initial term a0 is - an = aor∧n, n = 0,1, 2
In that case, if the general term for the given series is bn, we will have - bn+1 = 10.2n