Question

Which of the following sequences are in arithmetic progession ?

(i) 2,6,10,14, ........

(ii) 15,12,9,6,.........

(iii) 5,9,12,18,.......

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

Answer 1

For a sequence to be in AP

b-a=c-b

taking 1st sequence

6-2=4
10-6=4

so we can say 1st sequence is in Ap

Taking second sequence


12-15=-3

also 9-12=-3

hence 2nd sequence is also in AP

(III)

9-5=4

12-9=3

HERE B-A is not equal to C-B

so the sequence is not in AP


(iv)