Arithmetic Sequence. Finding a1 and d

Jul 2015
14
0
Riyadh, Saudi Arabia
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.

Please help. Thank you in advance (Talking)(Talking)
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey Lunatic.

What kind of equation are you trying to solve for?
 
Jul 2015
14
0
Riyadh, Saudi Arabia
Sorry for the late reply. I'm a bit of an idiot so I'll just go and state everything about this one.

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
Aug 2006
22,492
8,653
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 $2x+13x-60=0$
 
Jul 2015
14
0
Riyadh, Saudi Arabia
I'm at a lost here. What's the value of a1 and d then?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
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 $d=\frac{x}{2}$
 
Jul 2015
14
0
Riyadh, Saudi Arabia
Sorry the late reply(again)

Um, can I ask where'd you get the 13? Or maybe message me a step-by-step procedure.
 
Jul 2015
14
0
Riyadh, Saudi Arabia
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
Jun 2008
16,217
6,765
North Texas
\(\displaystyle a_n = a_1 + (n-1)d\)

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

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

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