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MrMuchimi
3 years ago
8

10. Dan picks 18 baskets of apples

Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

Answer:

1 basket = 24 apples

24 × 18 = 432 apples

(use cross multiplication method)

1 apple = 15 cents

432 = x

\frac{1x}{1}  = 6.480

x = 6.480 cents

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Find the 9th term of the geometric sequence 5, -25, 125, ...
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Or more accurately, it's a bit over 1.9 million.

===========================================================

Explanation:

  • a = 5 = first term
  • r = -5 = common ratio

Note that dividing any term by its previous term gets us the common ratio

  • r = term2/term1 = -25/5 = -5
  • r = term3/term2 = 125/(-5) = -5

The r value must stay the same the entire time, or else the sequence isn't geometric.

The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)

-----------------

To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.

If we tried n = 2 for instance, then we find the 2nd term is

5(-5)^(n-1) = 5(-5)^(2-1) = -25

which matches what your teacher gave you. I'll let you verify the other terms.

-----------------

The last thing we need to do is plug in n = 9 and simplify

5(-5)^(n-1)

5(-5)^(9-1)

5(-5)^8

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