The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,

-26

Step-by-step explanation:

Given the sequence:

16, 9, 2, –5, ...,

To find:

7th measurement, if the above sequence continues:

Solution:

Let us examine the given sequence first:

First term is 16

Second term = 9

Third term = 2

Fourth term = -5

Difference between 2nd and 1st term = 9 - 16 = -7

Difference between 3rd and 2nd term = 2 - 9 = -7

Difference between 4th and 3rd term = -5 - 2 = -7

We can see that there is a common difference of -7 between each term.

That means, the sequence is in Arithmetic Progression.

whose first term,

Common difference,

To find:

7th term i.e.

Solution:

Formula for term of an Arithmetic Progression is given as:

Let us put

7th measurement will be -26.

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step-by-step explanation:

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