Question

(look at screenshot)
Write an explicit rule and recursive rule for a geometric sequence with a second term of 6 and a third term of 12.

explicit:

recursive:

Answer 1

Answer:

Explicit : $a_n=3(2)^{n-1}$

Recursive: a₁ = 1

                  $a_n=a_{n-1}(2)$

Step-by-step explanation:

We have to write the recursive formula for the geometric sequence with second term 2 and third term 12.

Geometric sequence will be in the form of,

a, ar, ar², ar³,...........

Here, r = common ratio

a = first term of the sequence

Here, ar = 6 ------(1)

And ar² = 12 ------(2)

By dividing equation (2) by (1),

$\frac{ar^2}{ar}=\frac{12}{6}$

r = 2

From equation (1),

a(2) = 6

a = 3

Recursive formula of a geometric sequence is given by,

a₁ = a

$a_n=a_{n-1}(r)$

Therefore, for the given sequence,

a₁ = 1

$a_n=a_{n-1}(2)$

Similarly, explicit formula of the geometric sequence is given by,

$a_n=a_1(r)^{n-1}$

$a_n=3(2)^{n-1}$