UPSC NDA Math Model Paper 3

Given series is, 1+3−

1

2

+3+

1

3√3

.....
⇒a1=1,a2=

1

√3

,a3=3, a4=

1

3√3

....
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

≠

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.
⇒

1

a1

=1,

1

a2

=√3,

1

a3

=

1

3

etc..
⇒

1

a2

−

1

a1

=√3−1
⇒

1

a3

−

1

a2

=

1

3

−√3
Here,

1

a3

−

1

a2

≠

1

a2

−

1

a1

Given series 1+3−

1

2

+3+

1

3√3

.... is not HP
Hence, Given series 1+3−

1

2

+3+

1

3√3

..... is not AP, GP, HP