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Klio2033 [76]
3 years ago
13

Find the next 3 terms in the geometric sequence -36, 6, -1, 1/6, ...

Mathematics
1 answer:
timama [110]3 years ago
6 0

we are given

geometric sequence -36, 6, -1, 1/6, ...

first term is -36

a_1=-36

now, we can find common ratio

r=\frac{6}{-36}

r=-\frac{1}{6}

now, we can find nth term

a_n=a_1(r)^{n-1}

now, we can plug values

and we get

a_n=36(-\frac{1}{6})^{n-1}

now, we can find 5th term , 6th term, 7th term

fifth term:

a_5=36(-\frac{1}{6})^{4}

a_5=\frac{1}{36}

sixth term:

a_6=36(-\frac{1}{6})^{5}

a_6=-\frac{1}{216}

seventh term:

a_7=36(-\frac{1}{6})^{6}

a_7=\frac{1}{1296}

so, next terms are

a_5=\frac{1}{36} , a_6=-\frac{1}{216}

, a_7=\frac{1}{1296}.............Answer

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