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The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?

 May 11, 2024
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Let's find the common difference and the first term of the arithmetic sequence to determine the eighth term.

 

1. Find the common difference:

 

We know the fifth term (a₅) is 19 and the second term (a₂) is 17.

 

The common difference (d) can be found by subtracting the second term from the fifth term:

 

d = a₅ - a₂ = 19 - 17 = 2

 

2. Find the first term (a₁):

 

We can use the formula for any term (aₙ) in an arithmetic sequence: aₙ = a₁ + d(n - 1)

 

We know the second term (a₂ = 17) and the common difference (d = 2).

 

We can plug these values and n = 2 (since we're looking for the second term) to solve for a₁:

 

a₂ = a₁ + d(2 - 1) 17 = a₁ + 2(1) 17 = a₁ + 2 17 - 2 = a₁ = 15

 

3. Find the eighth term (a₈):

 

Now that we know the first term (a₁ = 15) and the common difference (d = 2), we can find the eighth term using the same formula:

 

a₈ = a₁ + d(8 - 1) a₈ = 15 + 2(7) a₈ = 15 + 14 a₈ = 29

 

Therefore, the eighth term in the arithmetic sequence is 29.

 May 11, 2024

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