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10th term of an arithmetic sequence is 24 and it's 14th term is 36. What is it's common difference?

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Answer:

common difference d = 3

Explanation:

the nth term of an arithmetic sequence is


a_(n) = a₁ + (n - 1)d

a₁ is the first term , d the common difference , n the term number

given a₁₀ = 24 and a₁₄ = 36

then we can write 2 equations and solve simultaneously

a₁ + 9d = 24 → (1)

a₁ + 13d = 36 → (2)

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

(a₁ - a₁ ) + (13d - 9d) = 36 - 24

0 + 4d = 12

4d = 12 ( divide both sides by 4 )

d = 3

then common difference d = 3

User Ramsay Smith
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