Sequence and series help please! (1 Viewer)

[YJ90]

Another question...thanks in advance!

1) In any geometric progression, show that the product of the first term and the last term is equal to the product of the second term and the last term but one.

 

[x3.eddayyeeee]

'but one' what?

 

[YJ90]

Thats the entire question. I assume one as in the number "1", lol. I dont know...

 

[jpmeijer]

Another question...thanks in advance!

1) In any geometric progression, show that the product of the first term and the last term is equal to the product of the second term and the last term but one.

The first term is:
T₁ = a

The second term is:
T₂ = ar

The last term is:
T_n = ar^n-1

The "last term but one" (the second last term) is:
T_n-1 = ar^n-2

So to answer the question, the product of the first term and the last term:
T₁*T_n = (a)*(ar^n-1) = a²r^n-1

and the product of the second term and the last term but one:
T₂*T_n-1 = (ar)*(ar^n-2) = a²r^n-1

are both equal to a²r^n-1

 

[YJ90]

Thankyou "jpmeijer"