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VashaNatasha [74]
3 years ago
9

1. A recursive formula for the sequence 40, 30, 22.5, ... is *

Mathematics
1 answer:
romanna [79]3 years ago
7 0

Answer:

Step-by-step explanation:

Given the sequence

40, 30, 22.5.......

We want to find the general formula for the sequence.

Let find out if it is arithmetic progression or Geometric progression

Arithmetic progression have a common difference e.g 2,5,8,11...., you will notice they have a common difference of 3.

So, let apply this to the given sequence

40, 30, 22.5.......

d = T2 - T1

d = 30 - 40 = -10

d = T3 - T2

d = 22.5 - 30 = -7.5

So, the difference are not equal, then it is not AP.

Let check for GP, GP have common ratio

r = T2 / T1 = 30 / 40 = 0.75

r = T3 / T2 = 22.5 / 30 = 0.75

Since the common ratio are equal, then, the sequence is GP

The nth term of a G.P is given as

Un = ar^(n-1)

Where

a is first term

r is common ratio

From the given sequence

40, 30, 22.5.......

a = 40 and r = 0.75

Then,

Un = a•r^(n-1)

Un = 40 × 0.75^(n-1)

From indices

a^b / a^c = a^(b-c)

Un = 40 × 0.75ⁿ / 0.75

Un = 53.333 × 0.75ⁿ

Un = 160•0.75ⁿ / 3

That is the nth term at any point

But if we want to find the next term given we know the previous term

From G.P

U1 = a

U2 = U1 × r = ar

U3 = U2 × r = ar × r = ar²

So, in this case r = 0.75 = ¾

So, the previous term multiply by ¾ will give the next term

Then,

Un = U(n-1) × 0.75

Un = ¾ U(n-1)

Un is next term

U(n-1) is previous term

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Answer:

Note: The full question is attached as picture below

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Answer:

Step-by-step explanation:

1.) y= 1/5x - 2

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How do I solve this math question? give full explanation using a formula. ​
lukranit [14]

Answer:

30 short cakes

Step-by-step explanation:

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each 10ml of milk can make us 12 short cakes

we can two 10ml of milk (20ml) which can make us 24 short cakes.

but we have 25 ml of milk so how much does 5ml of milk give us if 10ml of milk gives us 12 short cakes ?

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