What is the third item in the arithmetic sequence with first term 3 and common difference 4?

What is the third item in the arithmetic sequence with first term 3 and common difference 4?

• A. 7
• B. 8
• C. 11
• D. 12

Answer: (C)

To find the third item in an arithmetic sequence, you can use the formula for the \(n\)-th term of the sequence. The formula is given by: \[ a_n = a_1 + (n - 1) \cdot d \] where \(a_n\) is the \(n\)-th term, \(a_1\) is the first term, \(d\) is the common difference, and \(n\) is the term number. In this case, the first term \(a_1\) is 3, the common difference \(d\) is 4, and you want to find the third term, so \(n = 3\). Plugging these values into the formula gives: \[ a_3 = 3 + (3 - 1) \cdot 4 \] Calculating inside the parentheses first: \[ 3 - 1 = 2 \] Now substitute that back into the formula: \[ a_3 = 3 + 2 \cdot 4 \] Now calculate \(2 \cdot 4\): \[ 2 \cdot 4 = 8 \] Adding that

To find the third item in an arithmetic sequence, you can use the formula for the (n)-th term of the sequence. The formula is given by:

[

a_n = a_1 + (n - 1) \cdot d

]

where (a_n) is the (n)-th term, (a_1) is the first term, (d) is the common difference, and (n) is the term number.

In this case, the first term (a_1) is 3, the common difference (d) is 4, and you want to find the third term, so (n = 3).

Plugging these values into the formula gives:

[

a_3 = 3 + (3 - 1) \cdot 4

]

Calculating inside the parentheses first:

[

3 - 1 = 2

]

Now substitute that back into the formula:

[

a_3 = 3 + 2 \cdot 4

]

Now calculate (2 \cdot 4):

[

2 \cdot 4 = 8

]

Adding that