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Maths-

General

Easy

Question

After the first raffle drawing 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues, write an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?

hint Hint:

A sequence is said to be arithmetic if the common difference is always constant.

The General formula of any AP is $a subscript n equals a subscript 1 plus left parenthesis n minus 1 right parenthesis d$ .

The correct answer is: a_n=479.

Explanation:

We have given after the first raffle drawing, 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues.

We have to find an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?

Step 1 of 2:
We have given after the first raffle drawing, 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues.
It will form an AP with common difference
494 - 497 = -3
And First term is 497.
Now the explicit formula will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 497 plus left parenthesis n minus 1 right parenthesis left parenthesis negative 3 right parenthesis end cell row cell a subscript n equals 500 minus 3 n end cell end table$
Step 2 of 2:
After 7^th raffle drawing the ticket remains will be
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a subscript n equals 500 minus 3 n end cell row cell a subscript n equals 500 minus 3 left parenthesis 7 right parenthesis end cell row cell a subscript n equals 479. end cell end table$

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