- #1

ThomasMagnus

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**A finite geometric sequence has t1 = 0.1024 and t2 = 0.256. How many terms does this sequence have if its middle term has a value of 156.25?**

__My Solution__Common Ratio: T2/T1=(.256)/(.1024)=2.5

What term # is the middle term?

tn=ar^n-1

a=0.1024

r=2.5

tn=156.25

(156.25)=(0.1024)(2.5)^n-1

1525=(2.5)^n-1

[Log(1525)/Log(2.5)]+1=n

n=8+1=9

**n is the middle term so final term should be 2n. 18 terms in the sequence**

From the way I have seen other people do this question, they get the answer "17 terms". Why am I 1 term off? Can you help me with what I am doing wrong. Or am I doing it correctly :)

Thanks!