Question

Help please!!!!!!!!!!!!!

Answer 1

Answer:

position         1             5             8                12               19             25

term              -8            8             20             36               64            88

Step-by-step explanation:

(n - 1) is position ( n ∈ N)

d is the distance between the numbers in the sequence

a1 is the first number in the sequence

we have the fuction: a(n) = a1 + (n - 1)d

see in the table, with position = 1, term = -8 => a1 + d = -8

                                    position = 25, term = 88 => a1 + 25d = 88

=> we have: a1 + d = -8

                     a1 + 25d = 88

=> a1 = -12

    d = 4

=> a(n) = -12 + 4(n - 1)

=> term = 8, position = (8 + 12)/4 = 5

    position = 8, term = -12 + 4.8 = 20

    term = 36, position = (36 + 12)/4 = 12

    position = 19, term = -12 + 4.19 = 64

Answer 2

Answer:

The required table is:

Position   1     5       8      12      19      25

Term      -8     8      20     36     64     88  

Step-by-step explanation:

The general formula for arithmetic sequence is:

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

where n is the nth term, a₁ is the first term and d is the difference.

Looking at the table, we know that

a₁ = -8 and

a₂₅ = 88

We can find the common difference d:

$a_n=a_1+(n-1)d\\n=25, a_1=-8, a_{25}=88\\a_{25}=a_1+(25-1)d\\88=-8+24(d)\\88+8=24\:d\\96=24\:d\\d=\frac{96}{24}\\d=4$

So, we have d = 4

Now we can fill the remaining table.

We have to find position n, when term (a_n) is 8

$a_n=a_1+(n-1)d\\8=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\8+12=4n\\20=4n\\n=\frac{20}{4}\\n=5$

So, when term is 8, position is 5

We have to find term a_n when position n is 8

$a_n=a_1+(n-1)d\\a_8=-8+(8-1)4\\a_8=-8+7(4)\\a_8=-8+28\\a_8=20$

So, when position is 8 term is 20

We have to find position n, when term (a_n) is 36

$a_n=a_1+(n-1)d\\36=-8+(n-1)4\\8=-8+4n-4\\8=-12+4n\\36+12=4n\\48=4n\\n=\frac{48}{4}\\n=12$

So, when term is 36, position is 12

We have to find term a_n when position n is 19

$a_n=a_1+(n-1)d\\a_{19}=-8+(19-1)4\\a_{19}=-8+18(4)\\a_{19}=-8+72\\a_{19}=64$

when position is 19 term is 64

So, the required table is:

Position   1     5       8      12      19      25

Term      -8     8      20     36     64     88