How do you write an explicit formula for this sequence: 2, -1, 1/2, -1/4, 1/8?

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Answer 1 · 2016-04-30T08:52:06

This sequence is in GP
Since
The ratio of $"2nd Term"/"1st Term""=-1/2$

The ratio of $"3rdTerm"/"2nd Term"=(1/2)/-1=-1/2$

The ratio of $"4thTerm"/"3rdTerm"=(-1/4)/(1/2)=-1/2$
and so on
So the sequence has 1st term 2
and common ratio $-1/2$

If 1st term of GP be A and common ratio is r then its nth term is given by $t_n=ar^(n-1)$

If we put a =2 , r = $-1/2 and n=1$ we get $t_1=2xx(-1/2)^(1-1)=2$

If we put a =2 , r = $-1/2 and n=2$ we get $t_2=2xx(-1/2)^(2-1)=-1$

If we put a =2 , r = $-1/2 and n=3$ we get $t_3=2xx(-1/2)^(3-1)=1/2$