Isaak is trying to find the common ratio for the given sequence: 64, 112, 196, 343,...
A geometric sequence has a common ratio, which is the factor that each term is multiplied by to get the next term in the sequence. To find this common ratio, we need to divide each term by the preceding term.
Let's calculate the common ratio step by step:
1. Find the ratio of the second term to the first term:
- Second term: 112
- First term: 64
- [tex]\(\frac{112}{64} = 1.75\)[/tex]
2. Find the ratio of the third term to the second term:
- Third term: 196
- Second term: 112
- [tex]\(\frac{196}{112} = 1.75\)[/tex]
3. Find the ratio of the fourth term to the third term:
- Fourth term: 343
- Third term: 196
- [tex]\(\frac{343}{196} = 1.75\)[/tex]
We observe that the ratio between consecutive terms is consistently 1.75. Thus, the common ratio for the given sequence, rounded to the nearest hundredth, is:
[tex]\[
\boxed{1.75}
\][/tex]
So, Isaak should use 1.75 as the common ratio in the formula.
