How to write a rule for the sequence. Them, find the unknown term.
3/10,2/5--------,3/5,7/10
try using a common denominator:
3/10, 4/10, ... , 6/10, 7/10
now it's easy, right?
Tn = (n+2)/10
To write a rule for the given sequence, we need to look for a pattern in the terms.
For the given sequence:
3/10, 2/5, ----, 3/5, 7/10
We can notice that:
The numerators (top numbers) of the fractions are increasing by 1 in each term.
The denominators (bottom numbers) of the fractions are increasing by 5 in each term.
So, we can write the rule for this sequence as:
Numerator = 1st term numerator + (n-1)
Denominator = 1st term denominator + 5(n-1)
Now, let's find the unknown term using this rule:
The 1st term is: 3/10
To find the second term:
Numerator = 3 + (2-1) = 3
Denominator = 10 + 5(2-1) = 10 + 5 = 15
So, the second term is: 3/15
To find the fourth term:
Numerator = 3 + (4-1) = 3 + 3 = 6
Denominator = 10 + 5(4-1) = 10 + 15 = 25
So, the fourth term is: 6/25
To write a rule for the given sequence, we need to observe the pattern and determine how each term is related.
Looking at the sequence: 3/10, 2/5, --, 3/5, 7/10
We notice that each term is increasing by 1/10 from the previous term. Let's break it down to make it clear:
First term: 3/10
Second term: 3/10 + 1/10 = 2/5
Third term: 2/5 + 1/10 = ?
Fourth term: ? + 1/10 = 3/5
Fifth term: 3/5 + 1/10 = 7/10
As we can see, each term is obtained by adding 1/10 to the previous term.
Now, let's find the unknown term (the third term) by following the pattern.
Second term: 2/5
2/5 + 1/10 = 4/10 + 1/10 = 5/10
So, the unknown term (the third term) is 5/10.
To summarize, the rule for this sequence is to add 1/10 to the previous term. And the unknown term (the third term) is 5/10.