write an explicit formula for the nth term an for 17,20,23,26
OR
17, 20, 23, 26 is an arithmetic progression.
If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then the nth term of the sequence:
an = a1 + ( n - 1 ) * d
In this case the initial term a1 = 17, the common difference d = 3
an = a1 + ( n - 1 ) * d
an = 17 + ( n - 1 ) * 3
an = 17 + 3 * n - 3 * 1 = 17 + 3 n - 3 = 14 + 3 n = 3 n + 14
n = 1, a1 = 17 = 3 * 1 + 14 = 3 + 14
n = 2, a2 = 20 = 3 * 2 + 14 = 6 + 14
n = 3 , a3 = 23 = 3 * 3 + 14 = 9 + 14
n = 4 , a4 = 26 = 3 * 4 + 14 = 12 + 14
an = 3 n + 14
w h a t.
To find the explicit formula for the nth term (an) of the given sequence (17, 20, 23, 26), we can observe the pattern in the terms:
- The first term of the sequence is 17.
- The second term is obtained by adding 3 to the previous term: 17 + 3 = 20.
- The third term is obtained by adding 3 to the previous term: 20 + 3 = 23.
- The fourth term is obtained by adding 3 to the previous term: 23 + 3 = 26.
We can notice that the terms are increasing by 3 each time. Therefore, the explicit formula for the nth term an can be given as:
an = 17 + (n - 1) * 3
In this formula, n represents the position of the term in the sequence. For example, when n = 1, we get the first term: a1 = 17 + (1 - 1) * 3 = 17. Similarly, when n = 2, we get the second term: a2 = 17 + (2 - 1) * 3 = 20. And so on.