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40 votes
40 votes
What
arithmetic sequence with a_{4}=18 and a_{10}=48

User JPNagarajan
by
2.6k points

1 Answer

24 votes
24 votes

Answer:


a_(n) = 5n - 2

Explanation:

the nth term of an arithmetic sequence is


a_(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 18 and a₁₀ = 48 , then

a₁ + 3d = 18 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

6d = 30 ( divide both sides by 6 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3

Then


a_(n) = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2

User Nick Weisser
by
3.6k points
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