The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.
Answer Details
The nth term of a linear sequence can be expressed as follows:
nth term = a + (n-1)d
where a is the first term, d is the common difference and n is the number of terms.
In this question, the first term is 9 and the common difference is 7, so we have:
nth term = 9 + (n-1)7
We are told that the nth term is 380, so we can substitute this into the equation and solve for n:
380 = 9 + (n-1)7
380 - 9 = (n-1)7
371 = (n-1)7
n-1 = 371/7
n-1 = 53
n = 54
Therefore, the value of n is 54.