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.