SOLUTION: The 4th,5th and 6th terms of a linear sequence are 9-2x, x-2 and 2x-1 respectively. Find the: a) value of x b) 20th term c). nth term d) sum of 5th to 20th terms

Algebra ->  Sequences-and-series -> SOLUTION: The 4th,5th and 6th terms of a linear sequence are 9-2x, x-2 and 2x-1 respectively. Find the: a) value of x b) 20th term c). nth term d) sum of 5th to 20th terms      Log On


   

Question 934756: The 4th,5th and 6th terms of a linear sequence are 9-2x, x-2 and 2x-1 respectively. Find the:
a) value of x
b) 20th term
c). nth term
d) sum of 5th to 20th terms
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the 4th,5th,6th terms: p, q, r

p = 9-2x
q = x-2
r = 2x-1

If we subtract the 4th term from the fifth, we get q - p. That's equal to r - q since we have a common difference

so,

q - p = r - q

q+q = r+p

2q = r+p

2(x-2) = (2x-1)+(9-2x)

2x - 4 = 2x-1 + 9 - 2x

2x - 4 = 8

I'll let you finish up.