General formula for nth term in arithmetic sequence
an = a₁ + d(n - 1)
Given:
Arithmetic sequence with:
a₁ = 190
d = a₂ - a₁
d = 198 - 190
d = 8
Asked:
the rule and the 10th term
Solution
Find the rule of the sequence, use the general formula of nth term
an = a₁ + d(n - 1)
an = 190 + 8(n - 1)
an = 190 + 8n - 8
an = 8n + 182
The arithmetic sequence is determined with the rule 8n + 182 (n is the number of term)
Find the 10th term, use the rule
an = 8n + 182
a₁₀ = 8(10) + 182
a₁₀ = 80 + 182
a₁₀ = 262
The 10th term is 262