Friday, December 5, 2014

``8th term:` 1/2, -1/8, 1/32, -1/128...` Find the indicated term of the geometric sequence.

You may use the following formula, such that:


`a_n = a_1*r^(n-1)`


Replacing 8 for n,`1/2 ` for` a_1` yields:


`a_8 = 1/2*(r)^7`


You may find the ratio r, such that:


`r = (a_2)/(a_1) => r = (-1/8)/(1/2) => r = -1/4`


`a_8 = 1/2*(-1/4)^7 => a_8 = -1/(2^15)`


Hence, the indicated term `a_8 ` is `a_8 = -1/(2^15)`

You may use the following formula, such that:


`a_n = a_1*r^(n-1)`


Replacing 8 for n,`1/2 ` for` a_1` yields:


`a_8 = 1/2*(r)^7`


You may find the ratio r, such that:


`r = (a_2)/(a_1) => r = (-1/8)/(1/2) => r = -1/4`


`a_8 = 1/2*(-1/4)^7 => a_8 = -1/(2^15)`


Hence, the indicated term `a_8 ` is `a_8 = -1/(2^15)`

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