Question

In an arithmetic sequence, the first term, a_(1), is equal to 1 , and the seventh term, a_(7), is equal to 61 . Which number represents the common difference of the arithmetic sequence?

A) 8
B) 10
C) 9
D) 7

Answer 1

To find the common difference, we can use the formula a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference. By plugging in the values a_1 = 1 and a_7 = 61, we can solve for d and find that it is 10.

Step-by-step explanation:

To find the common difference of an arithmetic sequence, we can use the formula:

a_n = a_1 + (n-1)d

Where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.

In this case, we have a_1 = 1 and a_7 = 61. Plugging in these values, we get:

61 = 1 + (7-1)d

Simplifying the equation, we have:

60 = 6d

Dividing both sides by 6, we find that d = 10.

Therefore, the number that represents the common difference of the arithmetic sequence is B) 10.