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) About Me  (Show Source):
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The nth term of an arithmetic sequence is:
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
if the first term of an arithmetic sequence is -3 and the fifteenth term is 53, we have
a%5B1%5D=-3
a%5B15%5D=53
n=15
so,
53=-3%2B%2815-1%29d
53%2B3=14d

56=14d
d=56%2F14
d=4=> the common difference of the sequence


Answer by MathTherapy(10552) About Me  (Show Source):
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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: matrix%281%2C3%2C+a%5Bn%5D%2C+%22=%22%2C+a%5B1%5D+%2B+%28n+-+1%29d%29 

matrix%281%2C3%2C+a%5B15%5D%2C+%22=%22%2C+-+3+%2B+%2815+-+1%29d%29 --- Substituting matrix%282%2C3%2C+15%2C+for%2C+n%2C+-+3%2C+for%2C+a%5B1%5D%29

53 = - 3 + 14d ---------- Substituting matrix%281%2C3%2C+53%2C+for%2C+a%5B15%5D%29

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

d, or common difference = highlight_green%28matrix%281%2C3%2C+56%2F14%2C+%22=%22%2C+4%29%29

Answer by greenestamps(13200) About Me  (Show Source):
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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(52795) About Me  (Show Source):
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.
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  %2853+-+%28-3%29%29%2F14 = 56%2F14 = 4.    ANSWER

Solved.