Enter a recursive rule for the geometric sequence. 6, −18, 54, −162, ...

1 answer:

5 0

Answer:

The recursive formula needed is:

$a_n=(-3)\times a_{n-1}$

Detailed explanation:

We are given a geometric sequence:

6, -18, 54, -162, ...

By examining the terms, we see this sequence is a geometric progression (G.P.) with a common ratio, r, of -3.

Let $a_n$ denote the nth term.

This implies:

$a_1=6, a_2=-18, a_3=54, a_4=-162,......$

Since the common ratio equals -3,

therefore,

$a_1=6\\\\a_2=-18=(-3)\times a_1\\\\a_3=54=(-3)\times a_2\\\\.\\.\\.\\.\\.\\.\\.\\.\\.a_n=(-3)\times a_{n-1}$

Thus, the recursive formula for this geometric sequence is:

$a_n=(-3)\times a_{n-1}$

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AnnZ [12381]

Llen missed 5 targets, which is due to -50 divided by -10 equaling 5. I hope this clarifies! <3

6 0

2 months ago

tester [12383]

Response:

The width of the arch measures 105 meters

Detailed explanation:

The function that describes the width of the arch is

f(x) = -0.016(x - 52.5)² + 45

where x denotes the horizontal distance from the left end of the arch or the width at its base

f(x) indicates the vertical height of the arch

According to the given quadratic equation, the vertex coordinates of the parabola are (52.5, 45).

The vertex coordinates indicate that

the arch's height is 45 meters

and half the horizontal span from the left end is 52.5 meters

Therefore, the bridge's total width is calculated as 2 times the half span from the left side, which is 2 × 52.5

resulting in 105 meters

Consequently, the bridge's width is 105 meters.

4 0

2 months ago