Confused about the 1000th term of sequence 1,2,2 3,3.3,4,4,4... or propagation of electromagnetic (EM) waves?
Curious readers posed these questions in Topper's Ask The Expert section, and received an answer within three working days!
Subject: Maths
Q. Find the 1000th term of sequence 1,2,2,3,3,3,4,4,4,4...
Posted by: Thebluebloo
A. 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5...
|
Term value
|
Number of times
|
Cumulative Frequency
|
|
1
|
1 |
1 |
|
2
|
2 |
3 |
|
3
|
3 |
6
|
|
4
|
4 |
10
|
| .. |
.. |
.. |
|
n
|
n |
n(n+1)/2
|
Consider 1,3,6,10,...
Difference of the consecutive terms is an AP.
So applying the method of difference we get,
Tn = n (n+1) / 2
We need to find 1000th term
1000 = n(n+1)/2
n = 44.2
Its nearest integral value is 44.
So, 44 is the value of the 1000th term of the series 1,2,2,3,3,3,4,4,4,4...
Subject: Physics
Q. How are Electromagnetic (EM) waves propagated?
Posted by: Vipuljaglan
A. If an electric or magnetic field is constant then they can be analysed independently without looking at the interactions between them. But a time varying magnetic field acts as a source of electric field (Faraday's law) and a time varying electric field acts as a source of magnetic field (Ampere's law).
So, when either an electric or magnetic field is changing with time, a field of the other kind is induced in adjacent regions of space. These electromagnetic waves propagate through space from one region to another, even when there is no medium in the intervening region.
Subject: Chemistry
Q. What is stereoisomerism?
Posted by: Gnikhilvarma
A. Stereoisomers are isomeric molecules that have the same molecular formula and sequence of bonded atoms (constitution), but which differ in the orientation of their atoms in space.
