If I start with number 7 and count by 4s, the following sequence is obtained: 7, 11, 15, 19, 23, and so forth. A new sequence os formed when I start with a different number and count by a different number. Suppose the 2nd number of the new sequence is 8 and the 5th number is 17. What is the 10th number of the new sequence?
I need this problem sloved what is the answer
To find the 10th number of the new sequence, we need to determine the pattern in the sequence formed by starting with a different number and counting by a different number.
From the given information, we know that the 2nd number of the new sequence is 8 and the 5th number is 17. Let's try to determine the pattern:
To go from 8 to 17, we add 9 (17 - 8 = 9).
Therefore, the difference between consecutive terms in the new sequence is 9.
Now, let's calculate the first term in the new sequence:
To go back to the 1st term (also the term before the 2nd number in the new sequence), we need to subtract 9 from 8.
1st term = 8 - 9 = -1.
Since we have determined the difference between consecutive terms and the value of the 1st term, we can now find the 10th number in the new sequence:
To calculate the 10th term, we start with the 1st term (-1) and add the difference (9) for each subsequent term:
1st term: -1
2nd term: -1 + 9 = 8
3rd term: 8 + 9 = 17
4th term: 17 + 9 = 26
5th term: 26 + 9 = 35
6th term: 35 + 9 = 44
7th term: 44 + 9 = 53
8th term: 53 + 9 = 62
9th term: 62 + 9 = 71
10th term: 71 + 9 = 80.
Therefore, the 10th number of the new sequence is 80.
this is just a wordy way of describing an arithmetic progression with
a+d = 8
a+4d = 17
Solve for a and d, and then find
a + 9d