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a grasshopper jumps in a geometric sequence. each succeeding jump is 3/5 of the previous jump.if the grasshopper's jump is 30 cm, find the distance the grasshopper has covered after 5 jumps.

 Jul 27, 2016

Best Answer 

 #2
avatar+37144 
+10

30 x (3/5)^0 is the FIRST jump

30 x (3/5)^1  is SECOND jump

30 x (3/5)^2  is third jump

30 x (3/5)^3  is fourth jump

30 x (3/5)^4  is fifth jump

 

You can 'Brute Force' calculate and add up these numbers, or realize this is a summation of the form:

 

30 x  \(\sum_{1}^{5}\)(3/5)^(n-1) = 30 (2.3056) = 69.168 cm

 Jul 27, 2016
 #1
avatar
0

a grasshopper jumps in a geometric sequence. each succeeding jump is 3/5 of the previous jump.if the grasshopper's jump is 30 cm, find the distance the grasshopper has covered after 5 jumps

 

The grasshopper jumps the following distances:

30, 18, 10.8, 6.48, 3.89 =69.17cm in 5 jumps.

 Jul 27, 2016
 #2
avatar+37144 
+10
Best Answer

30 x (3/5)^0 is the FIRST jump

30 x (3/5)^1  is SECOND jump

30 x (3/5)^2  is third jump

30 x (3/5)^3  is fourth jump

30 x (3/5)^4  is fifth jump

 

You can 'Brute Force' calculate and add up these numbers, or realize this is a summation of the form:

 

30 x  \(\sum_{1}^{5}\)(3/5)^(n-1) = 30 (2.3056) = 69.168 cm

ElectricPavlov Jul 27, 2016
 #3
avatar
+10

It is a geometric series. Use the formula:

S=F(1 - r^n) / (1 - r)

S=30(1 - .6^5) /( 1 - .6)

S=30 x 2.3056

S=69.17 cm.

 Jul 27, 2016

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