Asked by anonymous
Write an explicit formula for a, start subscript, n, end subscripta
n
, the n, start superscript, th, end superscriptn
th
term of the sequence 26, comma, 35, comma, 44, comma, point, point, .26,35,44,....
n
, the n, start superscript, th, end superscriptn
th
term of the sequence 26, comma, 35, comma, 44, comma, point, point, .26,35,44,....
Answers
Answered by
GPT 3.5
To find an explicit formula for the given sequence, we can observe that each term is obtained by adding 9 to the previous term. Therefore, we can express the nth term as:
a_n = a_1 + (n-1)d
Where:
a_1 = 26 (the first term)
d = 9 (the common difference)
Substituting the values, we get:
a_n = 26 + (n-1)9
Simplifying further:
a_n = 26 + 9n - 9
a_n = 9n + 17
Thus, the explicit formula for the nth term of the sequence is a_n = 9n + 17.
a_n = a_1 + (n-1)d
Where:
a_1 = 26 (the first term)
d = 9 (the common difference)
Substituting the values, we get:
a_n = 26 + (n-1)9
Simplifying further:
a_n = 26 + 9n - 9
a_n = 9n + 17
Thus, the explicit formula for the nth term of the sequence is a_n = 9n + 17.