Enter a recursive rule for the geometric sequence. 4, -16, 64, -256, …

Solution:

Recursive formula for a geometric sequence is aₙ = a_n-1 r ,( n > or equal to 2) where ‘r’ is the common ratio.

In general a geometric series is represented as a, ar, ar², ar³, ………

Here a = 4 and ar = -16 ⇒ r = -4

Recursive rule will be a_n = a_n-1 x (-4)

Thus the given sequence is 4, (4)(-4), (4)(-4)², (4)(-4)³…….

Example: Enter a recursive rule for the geometric sequence. 5, -20, 80, -320, …

Recursive formula for a geometric sequence is aₙ = aₙ₋₁ r , where ‘r’ is the common ratio.

In general a geometric series is represented as a, ar, ar², ar³, ………

Here a = 5 and ar = -20 ⇒ r = -4

Recursive rule will be a_n = a_n-1 x (-4)

Thus the given sequence is 5, (5)(-4), (5)(-4)², (5)(-4)³…….

Enter a recursive rule for the geometric sequence. 4, -16, 64, -256, …

Summary:

Recursive rule for the geometric sequence. 4, -16, 64, -256, …is a_n = a_n-1 x (-4) , hence sequence can be written as 4, (4)(-4), (4)(-4)², (4)(-4)³…….