Question

Which of the following is the algebraic form of the arithmetic sequence 6, 10, 14, .... ?

• A. 4n + 1
• B. 6n + 4
• C. 5n + 1
• D. 4n + 2

Hint:

A quick way to check the options is to substitute n=1, n=2, etc., and see if you get the terms of the sequence.
For option (D) 4n + 2:
If n=1, a₁ = 4(1) + 2 = 6. (Correct)
If n=2, a₂ = 4(2) + 2 = 10. (Correct)
If n=3, a₃ = 4(3) + 2 = 14. (Correct)
This confirms the answer without deriving the formula.

Answer 1

The Correct Option is D

We need to find the algebraic expression for the n-th term (aₙ) of the given arithmetic sequence.

The formula for the n-th term of an arithmetic sequence (AP) is:
aₙ = a + (n-1)d where a is the first term and d is the common difference.

The given arithmetic sequence is 6, 10, 14, ....
The first term is a = 6.
The common difference is d = 10 - 6 = 4. (Also, 14 - 10 = 4).
Now, we substitute these values into the formula for the n-th term:
aₙ = 6 + (n-1)4 Distribute the 4:
aₙ = 6 + 4n - 4 Combine the constant terms:
aₙ = 4n + 2 The algebraic form of the sequence is 4n + 2.