Answer: the term number is 38
Step-by-step explanation:
Let the number of the term be x
The value of the xth term = 488
In an arithmetic sequence, the terms differ by a common difference, d. This means that the difference between two consecutive terms, d is constant.
The formula for the nth term is
Tn = a + (n-1)d
Where
Tn = the nth term of the arithmetic sequence
a = the first term of the arithmetic sequence.
d = common difference.
From the information given,
a = 7
d = 13
We are looking for the xth term.
Tx = 488 = 7 + (x-1)13
488 = 7 + 13x - 13
Collecting like terms on the left hand side and right hand side of the equation,
13x = 488 -7 + 13
13x = 494
x = 38
The value of the 38th term is 488.
