+8 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.
+37144 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
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.
+37144 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
