SOLUTION: Which term of the arithmetic sequence -10,-6,-2,2,6.... i s 94?

Algebra.Com
Question 1196371: Which term of the arithmetic sequence -10,-6,-2,2,6.... i s 94?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

Use the formula for the n-th term of an AP

     =  + (n-1)*d.


In your case   = -10,  d = 4,   = 94.


So, your equation is

    94 = -10 + (n-1)*4.


It gives

    94 + 10 = 4(n-1)

      104   = 4(n-1)

      n-1   = 104/4 = 26

       n    =         26 + 1 = 27.


ANSWER.  27-th term.

Solved.

-----------------

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You should understand the formal algebraic solution shown by the other tutor.

However, using formulas blindly doesn't teach you much about the actual problem. You should be able to use logical reasoning and simple arithmetic to get the answer (and to see why the formal solution gives the right answer).

The difference between -10 and 94 is 104; the common difference is the difference between -10 and -6, which is 4. 104/4 = 26; so 94 is 26 terms after the first term, making it the 27th term.

ANSWER: 27th
RELATED QUESTIONS

Find the nth term for this increasing arithmetic sequence: 2,4,6,8,10... (answered by greenestamps,math_tutor2020)
Determine the common difference, the fifth term, the nth term, and the 100th term of the... (answered by rfer)
The ninth term of the arithmetic sequence is 1/6 ; the sixteenth term is 2 ½. Find the... (answered by chana)
Find the 4th term of the arithmetic sequence with a base 1=-6 and... (answered by josgarithmetic)
Alpha writes the infinite arithmetic sequence 10, 8, 6, 4, 2, 0 ... Beta writes the... (answered by robertb)
The seventh term of an arithmetic sequence is 1/2 and the 14th term is 6. What is the... (answered by Cromlix,advanced_Learner)
the 7th term of an arithmetic sequence is 1/2 and the 14th term is 6 what is the 10th... (answered by rothauserc,Edwin McCravy,josmiceli)
Find the indicated term of each arithmetic sequence: 42nd term: a1 = 10; d = 6 I... (answered by checkley77)