How many terms are there in the following sequence?
12,15,18,...,57

Question

How many terms are there in the following sequence?
12,15,18,...,57

anonymous · Answer

16 terms.

Increase each previous term by 3 until you reach 57, then count the total number of terms.

anonymous · Answer

OR use...

tkhunny · Answer

Insufficient information.  You can ASSUME it is an arithmetic sequence, but there really is not enough information.

Maybe it's 12, 15, 18, 32, 75, 318.4, 9, 57

anonymous · Answer

$$a _{n}=a _{1}+(n+1)d$$

anonymous · Answer

It's probably not insufficient information, though I get your point @tkhunny. Which math are you taking @worthb214!?

tkhunny · Answer

It IS insufficient information.  The author of the problem should repent and do a better job at writing  questions.

anonymous · Answer

Digressing back to the formula. Plug in the last term (57) for $$a _{n}$$ and plug in the first term (12) for $$a _{1}$$. Then solve for 'n'.

anonymous · Answer

Its Math 102 for educators I don't know that is what the problem said.

tkhunny · Answer

For educators?  That's the PERFECT forum for discussing the inadequacies of the problem statement.  Excellent.  Bring it up and show your strength.

tkhunny · Answer

It can be fixed with one word.

How many terms are there in the following ARITHMETIC sequence? 12,15,18,...,57

anonymous · Answer

Like I said, it's 16. Use either of these two calculators to verify: http://www.basic-mathematics.com/arithmetic-sequence-calculator.html or http://www.calculator.net/number-sequence-calculator.html

anonymous · Answer

Did the question stem from a section titled "Arithmetic Sequences" or some derivation thereof?

anonymous · Answer

yeah that is what we are learning now is arithmetic and geometric sequences

anonymous · Answer

I mistyped the equation originally. It should read:
$$a _{n}=a _{1}+(n-1)d$$

57 = 12 + (n - 1)3

Distribute the 3 and you'll have:

57 = 12 + 3n - 3

Combine like terms that are already on the same side of the equal sign:

57 = 9 + 3n

Subtract 9 from both sides:

48 = 3n

Divide both sides by 3

16 = n

anonymous · Answer

okay thank you so much!

anonymous · Answer

This is a helpful page to checkout: http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm

anonymous · Answer

Take care!