Question

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, ...,

Answer 1

7th measurement= -26

Explanation:

The sequence is 16, 9, 2, –5, ...,

First term( a)= 16

Second term=9

Common difference (d) = 9-16

Common difference= -7

The sequence is a arithmetic progression

For AP's ,the terms formula is

Term(n) = a + (n-1)d

Where n represent the term to be found

In this case,we Are looking for the 7th term , so n= 7

Term(7) = 16+ (7-1)-7

Term(7)= 16 +6(-7).

Term (7) = 16-42

Term(7) = -26

7th term =-26

Answer 2

-26

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,
`a=16`

Common difference,
`d=-7`

To find:

7th term i.e.
`a_7=?`

Solution:

Formula for
`nth` term of an Arithmetic Progression is given as:

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

Let us put
`n=7`

`a_7=16+(7-1)* (-7)\\\Rightarrow a_7=16+6* (-7)\\\Rightarrow a_7=16-42\\\Rightarrow \bold{a_7=-26}`

7th measurement will be -26.