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Solution


Q.

Computer Animations: The animation on a new computer game initially allows the hero of the game to jump a (screen) distance of 10 inch over booby traps and obstacles. Each successive jump is limited to 3/4 inch less than the previous one.

Based on the above information, answer the following questions:

 

(i) Find the length of the seventh jump
1 512inch  
2 412inch  
3 -512inch  
4 432inch  

Ans.

(1)

Find the length of the thirteenth jump.

As the hero of the game initially jumps 10 inch and each successive jump is limited to 3/4 inch less than the previous one.

Therefore, we have

Distance covered in first jump = 10 inch

Distance covered in second jump = 10 − 3/4 = 37/4 inch

Distance covered in third jump = 37/4 − 3/4 = 34/4 inch and so on.

Clearly, these distances form an AP with a = 10 and d = −3/4

Length of 7th jump, a₇ = a + 6d= 10 + 6 × (−3/4)     = 10 − 9/2     = (20 − 9)/2= 11/2 inch = 512 inch.