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

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

$\Rightarrow$ arithmetic sequence is 40,36,32......

Since the common difference is -4, it algebraic expression is the form -4n+b

Consider n=1 $\Rightarrow$ -4(1)+b =First term

$\Rightarrow - 4 + b = 40$

$\Rightarrow b = 44$

$∴$ 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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