Question

1. Find 4 examples from an outside source of a real-world scenario that involves a sequence.
2. Define the sequence in three different ways.
3. Determine if the sequence is arithmetic, geometric, or neither.
4. Discuss which representation of the sequence is best in this real-world scenario, and why.

Answer 1

real world scenario examples for sequence:-

1)Weather forecasting:- Given a sequence of observations about the weather over time, predict the expected weather tomorrow.

2)Stock market prediction:- Given a sequence of movements of a security over time,predict the next movement of security.

3)Product recommendation: Given a sequence of past purchases of a customer,predict the next purchase of a customer.

4)example for arithmetic sequence in real life is person's birthday. the common difference is 1 year.

Define the sequence in three different ways:-

A sequence is ordered list of numbers.

(or)

A particular order in which related things follow each other.

(or)

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter.

sequences are different types:

1)arithmetic sequence

2)geometric sequence

3)harmonic sequence

1)arithmetic sequence:- The difference between any consecutive terms should be equal

ex:- 1 2 3 4 5...........

2 5 8 11 14...............

representation:- a,a+d,a+2d,a+3d...................., a+(n-1)d

nth term =a+(n-1)d

where d is the common difference

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2)geometric sequence:- The ratio between any consecutive terms should be same.

ex:- 2,4,8,16...............

3,6,9,12,15............

representation:- a,ar,ar²,ar³..............

where r is ratio of two consecutive numbers.

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3)harmonic sequence:- it is reciprocal of arithemetic sequence.

ex:-

representation:

-

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In real life scenario we mostly use geometric series.

We,ve seen that geometric series can get used to calculate the money how much you've got in the bank.

Infinite series have applications in engineering, physics, computer science, finance, and mathematics. In engineering, they are used for analysis of current flow and sound waves. In physics, infinite series can be used to find the time it takes a bouncing ball to come to rest or the swing of a pendulum to stop.