Anil played a game of space invaders. He scored points for each spaceship he
captured.
He scored 140 points for capturing first spaceship, 160 for second, 180 for third and
so on. The number of points scored for capturing each successive spaceship formed
a sequence.
a) Form the sequence using the above information and write the mathematical
concept used.
b) If capturing 20th spaceship gave Anil bonus of 100 points. How many points
did he score in total on capturing 20th spaceship?
c) How many total points Anil scored for capturing his first 20 spaceships
(excluding the bonus points).
Sunil his friend played an adventure game. He scored points for each dragon that he captured. The number of points that Sunil scored for capturing each successive
dragon formed a new sequence. Sunil captured n dragons and the total number of
points that she scored for capturing all n dragons was 8500.
Given that Sunil scored 300 points for capturing his first dragon and then 700 points
for his nth dragon.
d) Calculate the number of dragons Sunil captured for total 8500 points he
scored.
Answers
Given : Anil played a game of space invaders. He scored points for each spaceship he captured. He scored 140 points for capturing first spaceship, 160 for second, 180 for third and so on
capturing 20th spaceship gave Anil bonus of 100 points
To find : a) Form the sequence b) points he score in total on capturing 20th spaceship c) total points Anil scored for capturing his first 20 spaceships (excluding the bonus poi
Solution:
140 , 160 , 180 ,.......
a = 140
d = 20
AP
aₙ = a + (n - 1) d
a₂₀ = 140 + 19 * 20 = 520
520 + 100 bonus points = 620 score on capturing 20th spaceship
Sₙ = (n/2)(First Term + Last term)
= ( 20/2) ( 140 + 520)
= 6600
6600 scored for capturing his first 20 spaceships (excluding the bonus points)
____________________________
Sₙ = (n/2)(First Term + Last term)
(n/2)(300 + 700) = 8500
=> n = 17
Sunil captured 17 dragons
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