# 10th term of the arithmetic sequence -7, -1, 5,11, ... is______

embizze | Certified Educator

The nth term of an arithmetic sequence is given by `a_n=a_1+(n-1)d` where `a_1` is the first term of the sequence, and `d` is the common difference between two successive terms.

Given the sequence -7,-1,5,11,... we see that the common difference is6 (We add 6 to each term to get the next term), so d=6 and `a_1=-7`

So `a_10=-7+(10-1)(6)=-7+54=47`

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The tenth term of the sequence is 47

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-7,-1,5,11,17,23,29,35,41,47,...

Note that the terms of the sequence lie on a line; the common difference is the slope. Since the slope is 6 and we have the "point" (1,-7) we can find the equation of the line: `y-(-7)=6(x-1)` or `y=6x-13` . Then when x=10 we have y=60-13=47.

aishubuddy | Student

in the series -7, -1, 5,11, ... we can see tat the difference between 2 no's is 6. so thereby if we add 6 to each no ie. -7,-1,5,11,17,23,29,35,41,47.