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Geometric Series Can anyone solve this bugger?!?!

There is a geometric sequence 200,50......,0.1953125

the first term, a=200, common ratio, r=0.25

can anyone find the number of terms in the sequence??

Thanks, David

Reply 1

Christophicus

davidcy123

There is a geometric sequence 200,50......,0.1953125

the first term, a=200, common ratio, r=0.25

can anyone find the number of terms in the sequence??

Thanks, David

200(0.25)^n-1 = 0.1953125

Find n using logs.

Reply 2

davidcy123

Can you explain how I do this? Sorry Im just starting A-level maths. :mad:

Reply 3

Christophicus

davidcy123

Can you explain how I do this? Sorry Im just starting A-level maths. :mad:

A geometric series has first term a and consecutive terms ar,ar²,ar³,........,arⁿ

So in this example, a = 200 and r = 0.25

U₁ = a = 200
U₂ = ar = 200(0.25) = 50
U₃ = ar² = 200(0.25)² = 12.5
....
....
....
....
U_n = ar^n-1 = 200(0.25)^n-1 = 0.1953125

etc.

I set up an equation in n to express the final term in terms of a,n and r. a and r (and the value of the final term) are known but n is not. Have you encountered logs yet?