Enter a recursive rule for the geometric sequence. 10, -80, 640, -5120, …

Solution:

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 = 10 and ar = -80 ⇒ r = -8

Recursive rule will be a_n = a_n-1 x (-8)

Thus the given sequence is 10, (10)(-8), (10)(-8)², (10)(-8)³…….

Example: Enter a recursive rule for the geometric sequence. 15, -30, 60, -120, …

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 = 15 and ar = -30 ⇒ r = -2

Recursive rule will be a_n = a_n-1 x (-2)

Thus the given sequence is 15, (15)(-2), (15)(-2)², (15)(-2)³…….

Enter a recursive rule for the geometric sequence. 10, -80, 640, -5120, …

Summary:

Recursive rule for the geometric sequence. 10, -80, 640, -5120, …is a_n = a_n-1 x (-8) , hence sequence can be written as 15, (15)(-2), (15)(-2)², (15)(-2)³…….