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Question
A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then the algebra for the distance from the starting point to the ball after 't' seconds is
A ball starts to move along straight line at a speed of 40 metres/second and the speed decreases at the rate of 4 metres/second every second. Then the algebra for the distance from the starting point to the ball after 't' seconds is
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Solution
The correct option is D -4n+44
Distance covered in 1st sec =40 metres.
Distance covered in 2nd sec =(40-4)metres
=36 metres
Distance covered in 3rd sec =(40-4-4)meters.
=32 metres
⇒ arithmetic sequence is 40,36,32......
Since the common difference is -4, it algebraic expression is the form -4n+b
Consider n=1 ⇒ -4(1)+b =First term
⇒−4+b=40
⇒b=44
∴ Genral form is -4n+44
Verification: Arithmetic algebraic sequence is -4n+44
1st term =-4(1)+44 =40.
2nd term =-4(2)+44 =36.
3rd term =-4(3)+44 =32.
-4n+44
Distance covered in 1st sec =40 metres.
Distance covered in 2nd sec =(40-4)metres
=36 metres
Distance covered in 3rd sec =(40-4-4)meters.
=32 metres
⇒ arithmetic sequence is 40,36,32......
Since the common difference is -4, it algebraic expression is the form -4n+b
Consider n=1 ⇒ -4(1)+b =First term
⇒−4+b=40
⇒b=44
∴ Genral form is -4n+44
Verification: Arithmetic algebraic sequence is -4n+44
1st term =-4(1)+44 =40.
2nd term =-4(2)+44 =36.
3rd term =-4(3)+44 =32.
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