# arithmetic and geometric progression , classical problem

I need assistance in discerning sequences and series including the classical grains and checkboard problem

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:51 pm ad1c9bdddfhttps://brainmass.com/math/algebraic-geometry/arithmetic-geometric-progression-classical-problem-65625

#### Solution Preview

1) Use the arithmetic series of numbers 1, 3, 5, 7, 9,...to find the following:

a) What is d, the difference between any 2 terms?

Answer:

The difference between any two terms = ( n+1 )th term - ( n )th term

Hence , difference , d = 3-1 = 5-3 = 7-5 = 2

Answer d = 2

b) Using the formula for the nth term of an arithmetic series, what is 101st term? Answer:

nth term=a+(n-1)d..............(1)

Given a=first term=1

n=101

d=2

putting above values in formula 1

nth term=1+(101-1)*2

=1+200=201

Therefore , nth term = 201

Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?

Answer:

formula for the sum of an arithmetic series=n/2(2a +(n-1)d)..............(1)

given that , n = 20

a = first term = 1

Therefore , sum = 20/2(2*1+19*2)

=10*(40)

sum = 400

Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?

Answer:

formula for the sum of an arithmetic series=n/2(2a +(n-1)d)..............(1)

given that n = 30

a = first term =1

= 30/2(2*1+29*2)

...

#### Solution Summary

The solution contains answers to various questions involving A.P and G.P concepts including the famous classical problem involving checkboard and grains.