Question

D=? a1=? a5=86 a17=104​

Answer 1

An = A1+(n-1)d

A5 = A1+4d = 86

A17 = A1+16d = 104

{A1+16d = 104

-

{A1+4d = 86

12d = 18

D = 18/12 = 3/2 = 1.5

A1+6 = 86

A1 = 80

Answer 2

To find the common difference (D) and the first term (a1) of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1) * D

where: an = the nth term a1 = the first term D = the common difference n = the term number

Given the values of a5 = 86 and a17 = 104, we can set up two equations using the formula:

For the 5th term (n = 5): a5 = a1 + (5 - 1) * D 86 = a1 + 4D ...........(1)

For the 17th term (n = 17): a17 = a1 + (17 - 1) * D 104 = a1 + 16D ...........(2)

Now we have a system of two equations with two variables (a1 and D). We can solve this system to find the values.

Subtract equation (1) from equation (2) to eliminate a1:

104 - 86 = (a1 + 16D) - (a1 + 4D) 18 = 16D - 4D 18 = 12D

Now, divide both sides by 12 to solve for D:

D = 18 / 12 D = 1.5

Now that we have the common difference (D = 1.5), we can substitute it into equation (1) to find the value of a1:

86 = a1 + 4 * 1.5 86 = a1 + 6

Subtract 6 from both sides:

a1 = 86 - 6 a1 = 80

So, the common difference (D) is 1.5, and the first term (a1) is 80.