Thread: Formula for the n-th term . Sequence Question

Hi, I am new to this forum and I am also very new to math. I failed math in high school so my understanding of algebra is very weak. Even so, I would like to learn so please bare with me if I am being a nuisance.

Question

Find formula, showing all the work for the n-th term tn of the sequence (tn) . Defined with

t1 = 8; tn = ( 5*tn-1 ): 2; *tn-1 = previous term

I understand a little bit of this

GCSE Maths Sequences Revision - The nth Term | S-cool, the revision website

however, I can't seems to relate this with the question I am facing.

Any help is appreciated

Thank you for your time

Each term is 5 times higher than the previous term, sequences like these are called geometric sequences, since the first term is 8 and the common ratio is 5 the formula for the nth term is 8*5^n-1

Thanks a lot dude! that explains a lot

Sorry actually I am a bit lost

If t1 = 8; and tn = (5*tn-1) /2
Then t3 = (5*20)/2 = 50

But using the n-th term mentioned wont it be
t(3) = 8*5^n-1
= 8*5^2
= 8*25
= 400

I am very new to this, so I'm sorry if i misunderstood you somewhere

Originally Posted by RedGuitar

Sorry actually I am a bit lost
If t1 = 8; and tn = (5*tn-1) /2
Then t3 = (5*20)/2 = 50
But using the n-th term mentioned wont it be
t(3) = 8*5^n-1
= 8*5^2
= 8*25
= 400
I am very new to this, so I'm sorry if i misunderstood you somewhere

Your confusion results from your inability to post clearly what you mean.

Is it now

The formula given is

Originally Posted by RedGuitar

The formula given is

Why don't you see that

Oh I see it now,

How does sequence is normally solved? Do we eye ball for a pattern or is there a magic formula for it?

Plato can you please show me step by step to find the n term, please? I've been stuck with this for hours : (.

I tried to follow this Geometric Sequences and Series but I am still confused.

Originally Posted by RedGuitar

How does sequence is normally solved? Do we eye ball for a pattern or is there a magic formula for it?

Thanks a lot, I assume nth term = dn + (a - d) comes in play?

Thank you for your time everyone, it's been a great help

Originally Posted by RedGuitar

Thanks a lot, I assume nth term = dn + (a - d) comes in play?

Thank you for your time everyone, it's been a great help

That is for an arithmetic sequence, this is a geometric sequence.