SOLUTION: The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence? 14/13 25/7 4

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Question 1131527: The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?
14/13
25/7
4
Found 4 solutions by MathLover1, MathTherapy, greenestamps, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

The nth term of an arithmetic sequence is:

if the first term of an arithmetic sequence is and the fifteenth term is , we have



so,





=> the common difference of the sequence


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?
14/13
25/7
4
Specific term of an AP:  

 --- Substituting 

53 = - 3 + 14d ---------- Substituting 

56 = 14d ------------ Adding 3 to both sides

d, or common difference =  

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


Being able to use the formal algebraic methods to solve problems like this is important; you might need them for more difficult problems.  But for a simple problem like this one, you can do the same calculations without the formal formulas.


The 15th term is 14 terms after the 1st term (15-1 = 14).

The difference between the 15th term and the first term is 56 (53-(-3) = 56).

So the common difference is 56/14 = 4. 

Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
 .


There are 14 gaps of equal size between the first and fifteenth terms of arithmetic sequence.


So, each gap, which is the common difference, is   =  = 4.    ANSWER





Solved.





 

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