Question

The 20th term of an arithmetic sequence is 64 and its 21th term is 70. Can
the difference between two terms 46? Why?

Answer 1

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.