The 20th term of an arithmetic sequence is 64 and its 21th term is 70. Can
the difference between two terms 46? Why?
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Answer:
If the 20ᵗʰ term of the arithmetic sequence is 64 and its 21ᵗʰ term is 70, then its common difference cannot be 46 because 6 is the common difference of the given AP.
Step-by-step explanation:
For the given AP, let :
➤ First term be a
➤ Common difference be d
The 20ᵗʰ term of AP is 64, so :
➤ a₂₀ = 64
The 21ᵗʰ term of the AP is 70, so :
➤ a₂₁ = 70
We know that, common difference between two terms of an AP is :
➤ d = Second term — First term
➤ d = a₂₁ — a₂₀
➤ d = 70 — 64
➤ d = 6
∴ The common difference ‘d’ of the given AP is 6.
Hence, we can say that 46 can’t be the common difference between the terms of the given sequence.
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