Find the common difference and the SIMPLIFIED general term formula.
1 answer:
Answer:
= 100n - 78
Step-by-step explanation:
the nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₄ = 1322 and a₃₈ = 3722 , then
a₁ + 13d = 1322 → (1)
a₁ + 37d = 3722 → (2)
subtract (1) from (2) term by term to eliminate a₁
24d = 2400 ( divide both sides by 24 )
d = 100
substitute d = 100 into either of the 2 equations and solve for a₁
substituting into (1)
a₁ + 13(100) = 1322
a₁ + 1300 = 1322 ( subtract 1300 from both sides )
a₁ = 22
then nth term formula is
= 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78
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