PLEASE EXPLAIN HOW TO FIND THE COMMON RATIO FOR THE GEOMETRIC SEQUENCE

16, 40. 100,____, ____

AND

81,54, ______,______,______

40/16=2.5

100/4=2.5

2.5*100=250

250*2.5=625

16,40,100,250,625

81/54=1.5

81*1.5=121.5

121.5*1.5=182.25

182.25*1.5=273.375

81,54,121.5,182.25,273.375

To find the common ratio for a geometric sequence, you need to find the ratio between any two consecutive terms.

For the sequence 16, 40, 100, ____, ____, we can find the common ratio by dividing any term by its preceding term. Let's take the second and first terms:

Common ratio = 40 ÷ 16 = 2.5

So, the common ratio for this geometric sequence is 2.5.

Now, let's look at the sequence 81, 54, ______, _______, ______. In this case, you need to divide any term by its preceding term to find the common ratio. Let's take the second term and divide it by the first term:

Common ratio = 54 ÷ 81 = 0.666666...

This common ratio can be expressed as a fraction: 2/3 or as a decimal approximately: 0.67 (rounded to two decimal places).

Therefore, the common ratio for this geometric sequence is 2/3 or approximately 0.67.

To find the common ratio for a geometric sequence, there are two methods you can use. The first method involves dividing any term of the sequence by its preceding term, while the second method involves finding the ratio between any two consecutive terms. Let's use the second method for both of the sequences you provided.

1. Geometric Sequence: 16, 40, 100, __, __

To find the common ratio, we can divide any term by its preceding term:

40 / 16 = 2.5
100 / 40 = 2.5

Therefore, the common ratio for this geometric sequence is 2.5.

2. Geometric Sequence: 81, 54, __, __, __

To find the common ratio, we can again divide any term by its preceding term:

54 / 81 ≈ 0.67

Now we can use the common ratio to find the missing terms by multiplying:

54 * 0.67 ≈ 36.18
36.18 * 0.67 ≈ 24.23

Therefore, the missing terms in this geometric sequence are approximately 36.18 and 24.23.