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bonufazy [111]
4 years ago
12

Consuder the sequence that begins 40, 20, 10, 5

Mathematics
2 answers:
yulyashka [42]4 years ago
8 0
The explicit formula for a geometric sequence is usually written as:    an = ar(n – 1)        where   a=a1   and  r=common ratio a=80r=(1/2)    an = 80(1/2)(n=1) 80, 40, 20, 10, 5, 2 1/2, 1 1/4, 5/8, 5/16, ... note:  0.625 = 5/8 For some applications, the first element is A0, so you may encounter that preference.
dalvyx [7]4 years ago
5 0
The next on the sequence is 2.5
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Step 1: Assign variable for the unknown that  you need to find.

d_w \; \rightarrow \; Distance \; you \; traveled \; by \; walk \; in \; miles \\ d_c \; \rightarrow \; Distance \; traveled \; by \; your \; friend \; using \; bicycle \; in \; miles  \\ t \; \rightarrow \; Time \; Taken \; in \; hours

Step 2: List the given details

Distance between you and your friend is 12 miles. It means the total distance traveled by you by walk and your friend using bicycle when both travel towards each other to meet in 't' hours

Equation 1:

d_w+d_c=12

Your Walking rate and your friends Cycling rate is given below:

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Step 3: Set up an equation using the relationship between distance, time and rate.

Distance=Rate \times Time

d_w=r_w \times t=4t \\\\ d_c = r_c \times t = 11t

Substituting the above in equation 1

4t+11t=12 \\ Combining \; Like \; Terms \\\\ 15t=12 \\ Dividing \; 15 \; on \; both \; sides \\\\ 15t \div 15=12 \div 15 \\\\ t=0.8 hours

Distance traveled by you by walking from home and distance travelled by your friend in cycle in 0.8 hours is given below:

d_w=4t=4(0.8)=3.2miles \\\\ d_c=11t=11(0.8)=8.8miles

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