Question

Which of the following are in arithmetic progression?

• A. $2,6,10,14,.....$
• B. $15,12,9,6,.....$
• C. $5,9,12,18,.....$
• D. $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}.......$

Answer 1

Answer: (A), (B)

The correct options are
A $2,6,10,14,.....$
B $15,12,9,6,.....$

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.

Let us test the criteria for options given,

(A) $2,6,10,14,.....$

Here the difference of any two consecutive members is $4$. Hence this is an AP

(B) $15,12,9,6,.....$

Here the difference of any two consecutive members is $-3$. Hence this is an AP

(C) $5,9,12,18,.....$

Here the difference of any two consecutive members is not a constant$(9-5=4,12-9=3,18-12=6)$. Hence this is not an AP

(D) $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},.....$

Here the difference of any two consecutive members is not a constant$(\frac{1}{3}-\frac{1}{2}=\frac{-1}{6},\frac{1}{4}-\frac{1}{3}=\frac{-1}{12},\frac{1}{5}-\frac{1}{4}=\frac{-1}{20})$. Hence this is not an AP

Correct options are (A) and (B).