The first term of an arithmetic sequence is -1 and the 7^th term is 35 determine
1.The common difference of the sequence
2. The number of terms in the sequence if the last term of the sequence is 472
1. To find the common difference, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
Where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
Given that the first term a_1 = -1 and the 7th term a_7 = 35, we can plug these values into the formula:
35 = -1 + 6d
6d = 36
d = 6
So, the common difference of the sequence is 6.
2. To find the number of terms in the sequence, we can use the formula for the nth term of an arithmetic sequence again:
a_n = a_1 + (n-1)d
Given that the first term a_1 = -1, the common difference d = 6, and the last term a_n = 472, we can plug these values into the formula:
472 = -1 + (n-1)6
473 = 6n - 6
6n = 479
n = 79
So, the number of terms in the sequence is 79.