I am needing help with understanding this precalc question i

I am needing help with understanding this pre-calc question in my math. I tried looking over the provided examples with the unit, but i\'m stuck. the question is: The terms 5x + 2, 7x - 4 and 10x + 6 are consecuative terms of an arithmetic sequence. Determain the value of x and state the three terms ?

Thanks !!

Solution

Hi..

The consecutive terms of an arithmetic sequence are given as 5x+2,7x-4, and 10x+6.

Since this is an arithmetic sequence, the terms are a constant distance apart.

Thus (10x+6)-(7x-4)=(7x-4)-(5x+2)

3x+10=2x-6

x=-16

If x=-16, the terms are -78,-116,-154.

You could use the definition:

a(n)=5x+2

a(n+1)=7x-4

a(n+2)=10x+6

a(n+1)=an+d

7x-4=5x+2+d

d=2x-6

So a(n+2)=a(n+1)+d

10x+6=7x-4+2x-6

10x=6=9x-10

x=-16 as before.

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x=-16 so the terms are -78,-116,-154

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