Question

The terms 5x+2, 7x-4, and 10x+6 are consecutive terms of an arithmetic sequence. Determine the value of x and state the three terms.

I was just introduced to Tn=T1+(n-1)d so if I can answer using this equation that would be great

Answer 1

an arithmetical sequence has a common difference (d)
so in this case d = (7x - 4) - (5x + 2) = 2x - 6
also d = (10x + 6) - (7x - 4) = 3x + 10

therefore 2x - 6 = 3x + 10

do you follow this?

Answer 2

ok but would the difference between the T1 T2 T3 be the same?

Answer 3

yes t2 - t1 and t3 - t2 are the same - thats what an arithmetical sequence is

eg 2 , 4 , 6

Answer 4

ok I follow so far

Answer 5

now solve the equation to find x:

2x - 6 = 3x + 10
-6-10 = 3x - 2x

x = -16

now you can find the first 3 terms by plugging x= -16 into the terms in x

first one T1 = 5x+ 2 = 5(-16) + 2 = -78

Answer 6

now you can get the 2nd and third by plugging in x = -16 as above or you
can use the formula for Tn which you quoted in your question

Answer 7

awesome.Thanks for the help:)