Question

Given the first term and the common ratio of a geometric sequence, find the first five terms and write the explicit formula.
a1 = 1, r = 2

Answer 1

what?

Answer 2

That's the formula for the nth term of tier 1 geometric sequence

Answer 3

whats tn?

Answer 4

the nth term

Answer 5

\[T_{n} = a _{1} \times r ^{n - 1}\]

Answer 6

the first term is 1
the '`common ratio " is 2 so the second term is \(2\times 1=2\) ad the third term is \(2\times 2=4\) and so on

Answer 7

just keep multiplying by 2
\[1,2,4,8,16,32,...\]

Answer 8

@satellite73 are those the first five terms

Answer 9

The first term is a1 = 1
The second term a2 is the first term multiplied by the common ratio = 1 * r = 1 * 2 = 2
The third term a3 is the first term multiplied by (the common ratio) squared:
a3 = 1 * r * r = 1 * 2 * 2 = 4
The fouth term a4 is the first term multiplied by (the common ratio) cubed:
a4 = 1 * r * r * r = 1 * 2 * 2 * 2 = 8
The fifth term a3 is the first term multiplied by (the common ratio) to the power of 4:
a5 = 1 * 2 * 2 * 2 * 2 = you can calculate.

Answer 10

actually those are the first six terms, yes

Answer 11

so what's the explicit formula?

Answer 12

the 6th term is \(2^5=32\) ad i general the "nth" term is \(\large2^{n-1}\)

Answer 13

@satellite73 so is 2^(n-1) the explicit formula?

Answer 14

The general formula is
\[n ^{th}\ term=a _{1}\times r ^{n-1}\]