# Arithmetic Sequence. Finding a1 and d

#### Lunatic

This is one of the given numbers in my book:

a1 = x, d = 1/2x, a14 = 30

I can easily do this one:

a1 = x, d = 3x, a9 = 25

Since there are no fractions. But once there are fractions, I seriously can't find the answer anymore.

#### chiro

MHF Helper
Hey Lunatic.

What kind of equation are you trying to solve for?

#### Lunatic

The topic is about Arithmetic Sequences.

a1 is the first term, An is a specific term(so if we're looking for the 9th term, then it would be a9), d is the common difference(the d refers to the fact that the difference between two successive terms yields the constant value that was added).
e.g. 1,2,3,4,5,... find the 10th term.
a1 = 1, a10 = ?, d = 1.

The formula is:
An = a1 + (n-1)(d)
a10 = 1 + (10-1)(1)
a10 = 1+9
a10 = 10.

I could easily do this if all the terms are given, or maybe even with one or two of them is missing, but if one of the missing terms has fraction(1/2x), I just can't.

#### Plato

MHF Helper
This is one of the given numbers in my book:

a1 = x, d = 1/2x, a14 = 30
From the given: $x+13\left(\frac{x}{2}\right)=30$

OR $2x+13x-60=0$

#### Lunatic

I'm at a lost here. What's the value of a1 and d then?

#### skeeter

MHF Helper
I'm at a lost here. What's the value of a1 and d then?
Did you solve for x using the equation Plato set up?

note that $a_1=x$ and $d=\frac{x}{2}$

#### Lunatic

Um, can I ask where'd you get the 13? Or maybe message me a step-by-step procedure.

#### Plato

MHF Helper
can I ask where'd you get the 13? Or maybe message me a step-by-step procedure.
Sorry but I refuse to promote laziness.

#### Lunatic

From the given: $x+13\left(\frac{x}{2}\right)=30$

OR $2x+13x-60=0$
I get two different results from the two formulas. I get 15/2 on the first formula and 4 in the second formula. What did I do wrong?

#### skeeter

MHF Helper
$$\displaystyle a_n = a_1 + (n-1)d$$

$$\displaystyle a_{14} = a_1 + (14-1)d$$

$$\displaystyle a_{14} = 30$$ , $$\displaystyle a_1 = x$$ , $$\displaystyle d = \frac{x}{2}$$

substitute the three terms above into the second equation and you'll get the equation Plato set up.