What is the next fraction in this sequence? Simplify your answer. 9/10, 4/5, 7/10, 3/5....

Question

please help me solve this question and find the next term please, sequence fractions are complicated :(

Answer 1

A third way:

Notice that for this set of numbers, the denominators have a least common multiple of 10. Convert all of the fractions to 10ths:

So the sequence would be 9/10, 8/10, 7/10, 6/10. The next number would be 5/10, which is equal to 1/2. That's the final answer.

Answer 2

There are two ways to do this. First you need to make sure it is an arithmetic sequence. To do this you need to show that the numbers in the sequence have a common difference. Meaning you add or subtract a number it will get you the next number in the sequence.

First way you can do this:

1) Turn all the fractions into decimals

9/10 = 0.9 4/5 = 0.8 7/10 = 0.7 3/5 = 0.6

2) Take the first term (a₁) and subtract it from the next term (a₂)

a₁ - a₂ = 0.9 - 0.8 = 0.1 d = 0.1

3) Now you take the last term that you know and subtract the difference (d)

0.6 - d = 0.6 - 0.1 = 0.5

4) Now you convert the decimal you got into a fraction.

0.5 = 1/2

So the next term in the Sequence is 1/2

The second why you can do this is:

1) Turn all the fractions into decimals

9/10 = 0.9 4/5 = 0.8 7/10 = 0.7 3/5 = 0.6

2) Take the first term (a₁) and subtract it from the next term (a₂)

a₁ - a₂ = 0.9 - 0.8 = 0.1 d = 0.1

3) Plug the information you have into the following formula

a_n = a₁ + (n - 1)d

a_n = n^th term a₁ = first term d = common difference

the nth term is the term you are looking for. you have 4 terms and you are looking

for the 5^th

n = 5 a₁ = 0.9 d = 0.1

a₅ = 0.9 + (5 - 1) 0.1

= 0.9 + (4) 0.1

= 0.1 + 0.4

= 0.5

4) Now you convert the decimal you got into a fraction.

0.5 = 1/2

So the next term in the Sequence is 1/2