Question

For an arithmetic sequence, a_5
= 16, and a_8 =32. Find the common difference.

Answer 1

To find the common difference in an arithmetic sequence, substitute the given terms into the formula a_n = a_1 + (n-1)d and solve for d and we get the common difference is 16/3.

Step-by-step explanation:

To find the common difference in 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 term number, and d is the common difference.

In this case, we are given that a_5 = 16 and a_8 = 32. Substituting these values into the formula, we can solve for the common difference:

1. 16 = a_1 + (5-1)d
2. 32 = a_1 + (8-1)d

By subtracting the two equations, we can eliminate a_1 and solve for d:

1. 16 - 32 = (5-1)d - (8-1)d
2. -16 = 4d - 7d
3. -16 = -3d
4. d = -16/-3 = 16/3

Therefore, the common difference is 16/3.