.... A sequence of numbers is called an arithmetic progression if the difference between any two consecutive terms is always same. ⇒a2−a1=
1
√3
−1=
1−√3
√3
Now, a3−a2=3−
1
√3
=
3√3−1
√3
Here, a2−a1≠a3−a2 Given series 1+3−
1
2
+3+
1
3√3
... is not AP Now, A sequence of numbers is called a geometric progression if the ratio of any two consecutive terms is always same.
a2
a1
=
1
√3
a3
a2
=
3
1
√3
=3√3 Here,
a3
a2
â‰
a2
a1
Given series 1+3−
1
2
+3+
1
3√3
.... is not GP A sequence of numbers is called a harmonic progression if the reciprocal of the terms are in AP. In simple terms, a,b,c,d,e,f are in HP if 1/a, 1/b, 1/c, 1/d, 1/e, 1/f are in AP. ⇒