Question

Find n-th term of series 1, 3, 6, 10, 15, 21 c code

Answer 1

Answer:

Step 1

Find the degree of the sequence.

This can be done by writing down the sequence of common difference until you receive a arithmetic sequence.

For eg. in the case of 1,3,6,10,15,21…

CD1: 2,3,4,5,6..

CD2: 1,1,1,1,1,…

This implies that the sequence behaves like a second degree polynominal.

NOTE: If we get AP in CDn the polynominal has a degree of n

Step 2

The nth term can found by using the property of the CD sequences

As the common difference is n+1 th term - nth term.

eg.

As, the nth term is in second degree common difference equals,

a(n+1)^2 + b(n+1) + c - an^2 + bn + c = 2an + a+b —(1)

now consider CD1,

from there we can say,

a+b =1

2a = 1

i.e,

a=1/2

b=1/2

the nth term is

1/2*n^2 + 1/2*n

where n ={0,1,2,3,..}

Step-by-step explanation: