What is the relation between any two consecutive terms?
Pattern: Geometric Next Term: a_5=16 Rule for the nth Term: a_n=2^(n-1)
Practice makes perfect
Let's start by paying close attention to the terms of the given sequence.
cccc
a_1 && a_2 && a_3 && a_4
1 &→& 2 &→& 4 &→& 8
We can see that the ratio between any two consecutive terms is always 2. Therefore, we have a geometric sequence with a common ratio of 2. To find the 5th term, we will multiply the value of the 4th term by 2.
a_5=8 * 2=16
Finally, considering that we have a geometric sequence with a first term of 1 and a common ratio of 2, we can write its rule.
a_n= a_1 r^(n-1)
⇓
a_n= 1 * 2^(n-1)
a_n=2^(n-1)
