Question

For the sequence attached, find the value of the 20th term.

Answer 1

Question C

Answer 2

Every term, you're taking the last term and multiplying it by 3. You're doing this 19 times (not 20, because you already know the 1st term).

So...there's a quick way to multiply by 3 19 times. What do you think the answer is?

Answer 3

No idea.

Answer 4

I was thinking powers

Answer 5

Yes, 3^19 is the same as multiplying by 3 19 times.

Answer 6

but the 1st value is 2

Answer 7

is there a general formula?

Answer 8

they give you instructions:
the first term u1=2
the i+1 term \( u_{i+1}= 3u_i \)
that means to multiply the previous term by 3.
now start writing down the terms:
u1= 2 (given)
u2= 3*u1= 3*2= 6
u3= 3*u2= 3*3*2= 18
and so on

now look for the pattern for u_n

Answer 9

Right, the first value is 2...you're multiplying 2 by 3 19 times, or 2 by (3^19).

Answer 10

many thanks.