## Anil played a game of space invaders. He scored points for each spaceship he captured. He scored 140 points for capturing first spaceship, 1

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 oncapturing 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 poiSolution:140 , 160 , 180 ,…….

a = 140

d = 20

APaₙ = a + (n – 1) d

a₂₀ = 140 + 19 * 20 = 520

520 + 100 bonus points =

620 score on capturing 20th spaceshipSₙ = (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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