Question

Suppose {a} n Є No is an arithmetic sequence and a3=2, a5=8. What is the common difference of this arithmetic sequence?

3
6
4
2

Answer 1

To find the common difference of the arithmetic sequence, use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d. Given a3 = 2 and a5 = 8, solve the system of equations to find the common difference.

Step-by-step explanation:

To find the common difference of the arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

We are given that a3 = 2 and a5 = 8. Substituting these values into the formula, we have:

2 = a1 + (3-1)d
8 = a1 + (5-1)d

Simplifying the equations, we get:

2 = a1 + 2d
8 = a1 + 4d

From here, we can solve the system of equations to find the values of a1 and d. Subtracting the first equation from the second equation, we get:

6 = 2d
d = 3

Therefore, the common difference of the arithmetic sequence is 3.

Answer 2

The common difference of the arithmetic sequence is 3. Option 1 is correct.

To solve this problem

We are aware that an arithmetic sequence has the general form
`a_n = a_1 + d(n - 1),` where d is the common difference and
`a_1` is the first term.

With the information provided, we can construct two equations:

• Equation 1: a3 = a1 + 2d = 2 (since a3 = 2)
• Equation 2: a5 = a1 + 4d = 8 (since a5 = 8)

To determine the common difference (d), we can solve these two equations simultaneously.

Subtracting Equation 1 from Equation 2, we get:

2d = 6

Dividing both sides by 2, we get:

d = 3

So, the common difference of the arithmetic sequence is 3.