What is the 14th term of the sequence 14, 10, 6, 2, ... ?

Question

What is the 14th term of the sequence 14, 10, 6, 2, ... ?

1. A. -42
2. B. -34
3. C. -46
4. D. -38 (Correct answer)

Correct Answer

Option D — -38

Detailed Solution & Explanation

The correct answer is -38.

Key Points

• The sequence 14, 10, 6, 2, ... is an Arithmetic Progression (AP) with first term a = 14 and a common difference d = -4 (each term is 4 less than the previous one).
• The nth term of an AP is given by the formula aₙ = a + (n - 1)d.
• For the 14th term:
• aₙ = 14 + (14 - 1) × (-4) = 14 + 13 × (-4) = 14 - 52 = -38.

Exam Tip

• always identify a and d first, then plug straight into a + (n-1)d — here 13 steps of -4 from 14 lands exactly on -38, confirming option (D).

Additional Information

• Use the AP formula aₙ = a + (n − 1)d: with a = 14, d = −4 and n = 14, a₁₄ = 14 + 13(−4) = −38.
• Confirm the common difference from more than one consecutive pair before applying the formula — 10 − 14 = −4 and 6 − 10 = −4.
• The companion formulas worth memorising: sum Sₙ = n/2 [2a + (n − 1)d], and for the last term Sₙ = n/2 (a + l).