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Answer:
Finding the 30th Term of an Arithmetic Sequence
Understanding the Problem
We're given:
* The 5th term (a₅) is -10
* The common difference (d) is 6
We need to find the 30th term (a₃₀).
Solution
1. Find the first term (a₁):
We can use the formula for the nth term of an arithmetic sequence:
* aₙ = a₁ + (n - 1)d
Substituting the given values:
* -10 = a₁ + (5 - 1)6
* -10 = a₁ + 24
* a₁ = -34
2. Find the 30th term (a₃₀):
Using the same formula:
* a₃₀ = -34 + (30 - 1)6
* a₃₀ = -34 + 174
* a₃₀ = 140
Therefore, the 30th term of the arithmetic sequence is 140.