James deposited some money into a savings account to save for a motorcycle. Based on the interest rate of the account, he estimates that his money will grow according to the following table.
Years Value
1 $1428
2 $1457
3 $1486
4 $1516
5 $1546
The values follow a geometric sequence. What is the common ratio of the sequence?
1457/1428 = 1.0203..
1486/1457 = 1.0199..
1516/1486 = 1.0202
1546/1516 = 1.0198
looks like about 1.02 to me, all the monies are rounded to the nearest dollar.
Have you considered dividing a value by its previous one ??
I tried and got 1.01, but I don't know if it is correct
Thank you so much!!!
To find the common ratio of a geometric sequence, you need to divide any term in the sequence by the term that comes before it. In this case, let's divide each value by the previous value to find the common ratio.
The term "common ratio" refers to the number that each term is multiplied by to get the next term in a geometric sequence.
Let's divide each value by the previous value:
1428 / 0 = undefined
1457 / 1428 ≈ 1.02027297
1486 / 1457 ≈ 1.01988382
1516 / 1486 ≈ 1.02016129
1546 / 1516 ≈ 1.01973684
As we can see, the values are approximately equal to each other, indicating that there is a common ratio between them.
Rounding the decimals to a reasonable degree of accuracy, we can see that the values are all around 1.02. Therefore, the common ratio of this geometric sequence is approximately 1.02.