9, 13, 17, 21, ...
In the sequence above, each term after the first is 4 greater than the previous term. What is the difference between the 105th term and the 99th term?
I have no idea how to solve this problem
To find the difference between the 105th term and the 99th term, we need to first find the values of these terms.
Given that each term after the first is 4 greater than the previous term, we can find the value of any term by adding 4 to the previous term.
Now let's find the value of the 99th term:
First term: 9
Second term: 9 + 4 = 13
Third term: 13 + 4 = 17
and so on...
To find the 99th term, we need to apply the pattern 96 times, since the second term is the 96th term, the third term is the 97th term, and so on.
99th term = 9 + (96 * 4)
Now let's find the value of the 105th term:
105th term = 9 + (104 * 4)
Now we can calculate the difference between the 105th term and the 99th term:
Difference = 105th term - 99th term
I will now proceed to calculate the difference.
To find the difference between the 105th term and the 99th term in the sequence, you can use the formula for arithmetic sequences:
Term = First Term + (n - 1) * Common Difference
First, let's determine the first term and the common difference. The first term in the sequence is 9, and the common difference is 4, as stated in the problem.
Now, let's calculate the 99th term and the 105th term using the formula:
99th term = First term + (99 - 1) * Common difference
105th term = First term + (105 - 1) * Common difference
99th term = 9 + (98) * 4 = 9 + 392 = 401
105th term = 9 + (104) * 4 = 9 + 416 = 425
Finally, to find the difference between the 105th term and the 99th term, subtract the value of the 99th term from the 105th term:
425 - 401 = 24
Therefore, the difference between the 105th term and the 99th term is 24.