What is the eighth term of an arithmetic sequence with a first term of 10 and a third term of 22?

What is the eighth term of an arithmetic sequence with a first term of 10 and a third term of 22?

• A. 42
• B. 52
• C. 62
• D. 72

Answer: (B)

In an arithmetic sequence, each term can be expressed in terms of the first term and the common difference. The formula for the nth term of an arithmetic sequence is given by: \[ a_n = a_1 + (n - 1) d \] where \( a_n \) is the nth term, \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number. In this sequence, we know the first term \( a_1 \) is 10. The third term \( a_3 \) is given as 22. Using the formula for the third term: \[ a_3 = a_1 + (3 - 1) d \] Substituting the known values: \[ 22 = 10 + 2d \] To find the common difference \( d \), we can rearrange this equation: \[ 22 - 10 = 2d \] \[ 12 = 2d \] \[ d = 6 \] Now that we have the common difference, we can find the eighth term using the same formula: \[ a_8 = a_1 + (8 - 1)

In an arithmetic sequence, each term can be expressed in terms of the first term and the common difference. The formula for the nth term of an arithmetic sequence is given by:

[ a_n = a_1 + (n - 1) d ]

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

In this sequence, we know the first term ( a_1 ) is 10. The third term ( a_3 ) is given as 22. Using the formula for the third term:

[ a_3 = a_1 + (3 - 1) d ]

Substituting the known values:

[ 22 = 10 + 2d ]

To find the common difference ( d ), we can rearrange this equation:

[ 22 - 10 = 2d ]

[ 12 = 2d ]

[ d = 6 ]

Now that we have the common difference, we can find the eighth term using the same formula:

[ a_8 = a_1 + (8 - 1)