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Find the 5th term of the arithmetic sequence with a7=25 and a3 =55.
Question
Find the 5th term of the arithmetic sequence with a7=25 and a3 =55.
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Mathematics
6 months
2021-07-28T02:55:33+00:00
2021-07-28T02:55:33+00:00 1 Answers
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Answer:
a₅ = 40
Step-by-step explanation:
The n th term of an arithmetic sequence is
where a₁ is the first term and d the common difference
Given a₇ = 25 and a₃ = 55 , then
a₁ + 2d = 55 → (1)
a₁ + 6d = 25 → (2)
Subtract (1) from (2) term by term to eliminate a₁, then
4d = – 30 ( divide both sides by 4 )
d = – 7.5
Substitute d = 7.5 into (1)
a₁ + 2(- 7.5) = 55
a₁ – 15 = 55 ( add 15 to both sides )
a₁ = 70
Thus
a₅ = 70 – 7.5(4) = 70 – 30 = 40