Question

Kenny's scores the first 5 times he played a video game are listed below. 38, 51, 64, 77, 90 Kenny's scores follow a pattern. If the pattern continues, what would be Kenny's score on his 72nd game played?

Answer 1

Kenny's score on his 72nd game played is 961

Solution:

Given that the first 5 score of Kenny are listed below:

38, 51, 64, 77, 90

Kenny's scores follow a pattern

To find: Kenny's score on his 72nd game played

Let us first find the pattern followed

38, 51, 64, 77, 90

Find the difference between terms

51 - 38 = 13

64 - 51 = 13

77 - 64 = 13

90 - 77 = 13

So the difference between terms is constant

So the sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

The formula for nth term of arithmetic sequence is given as:

`a_n = a_1 + (n-1)d`

`a_n` = the nᵗʰ term in the sequence

`a_1` = the first term in the sequence

d = the common difference between terms

Here d = 13 and
`a_1 = 38`

So we get,

`a_n = 38 + (n-1) * 13`

To find the score of 72nd game, substitute n = 72

`a_(72) = 38 + (72-1) * 13\\\\a_(72) = 38 + 71 * 13\\\\a_(72) = 38 + 923\\\\a_(72) = 961`

Thus Kenny's score on his 72nd game played is 961