+121 The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is the eighth term?
+1725 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.
