A problem on geometric sequence

If a sequence of values follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term, it is referred to as a geometric sequence. The number multiplied each time is constant .

The fixed amount multiplied is called the common ratio, r, referring to the fact that the ratio (fraction) of the second term to the first term yields this common multiple. To find the common ratio, divide the second term by the first term.

Let's a example on this.

Question:-

What is the next term in the geometric sequence 16,-4,1,-1/4

Answer:-

given terms 16,-4,1,-1/4

first term = a =16

common ratio=r= t2/t1

r = -4/16 = -1/4

5 th term =r5=a*r^5-1

= 16*(-1/4)⁴

=16*(1/256)

= 1 / 16 is the answer

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