SOLUTION: given the progression , m-1, 2m,3m+1, 4m+2..., determine the common difference the 20th term in term of m the value of m, hence give the numerical values of the 1st three terma

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Question 1029350: given the progression , m-1, 2m,3m+1, 4m+2..., determine
the common difference
the 20th term in term of m
the value of m, hence give the numerical values of the 1st three terma
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the common difference is m+1

the formula for the nth term of an arithmetic progression is An = A1 + (n-1)d

the 20th term would therefore be A20 = A1 + 19d

A1 is equal to m-1.

the formula becomes A20 = m-1 + 19d

d = m+1

the formula becomes A20 = m-1 + 19 * (m+1)

simplify to get A20 = m-1 + 19m + 19

simplify further to get A20 = 20m + 18.

it appears that m can be any number.

for example:

if m = 1, then d = m + 1 = 2 and.....
the first number is m-1 = 0
the second number is 0 + (2-1)*2 = 2
the third number is 0 + (3-1)*2 = 4
etc.

if m = 2, then d = m + 1 = 3 and ....
the first number is m-1 = 1
the second number is 1 + (2-1)*3 = 4
the third number is 1 + (3-1)*3 = 7
etc.

as far as i can tell, you can pick any number for m and the sequence is valid.

i tried it with positive numbers and negative numbers and it appears to work with both.