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gavmur [86]
2 years ago
14

I Will BE GIVING A BRAINLIST AND A FOLLOW BACK ONLY FOR THE ACCURATE ANSWERS PLEASE TAKE A LOOK AT MY WORKSHEET PLEASE ANSWER QU

ESTIONS 1-5 AND PROVIDE EXPLANATION .

Mathematics
1 answer:
Vesna [10]2 years ago
4 0

Answer:

1. Recursive formula: b(n-1)+2

2. Explicit formula: −2n+5

3. -20

4. 2, 11, 20, 29, 38, 47, 56, 65, 74, 83, 92, 101, 110, 119, 128

Step-by-step explanation:

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The sum of the second and third terms of G.P is six times the fourth term. Find the two possible values of the common ratio​
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Answer:

Step-by-step explanation:

Let “a” be the first term and ”r” the common ratio of the GP. Then,

f(n) = ar^(n - 1).

f(2) + f(3) = 6f(4). (given)

ar + ar^2 = 6ar^3, or

1 + r = 6r^2, or

6r^2 - r - 1 = 0,

(3r + 1)(2r - 1) = 0.

r = -1/3, or 1/2.

If the common ratio is positive and the second term is 8 we have,

ar = 8, or

a*1/2 = 8, or a = 16.

f(n) = 16*(1/2)^(n - 1) = 2^4*2^(1 - n), or

f(n) = 2^(5 - n).

The first six terms of the GP are : 16, 8, 4, 2, 1, 1/2,…

××××××××××

Checking : f(2) + f(3) = 6f(4), (given).

LHS = 8 + 4 = 12.

RHS = 6* 2 = 12.

LHS = RHS.

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Step-by-step explanation:

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