Question

Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37.

an = -2 + (n-1)(-5)
an = -2 + (n-1)(5)
an = 2 + (n-1)(-5)
an = 2 + (n-1)(5)

Answer 1

the correct answer is an = -2 + (n-1)(-5). option A

Answer 2

Option A is correct

General rule for arithmetic sequence with
`a_3 = -12` and
`a_8 = -37` is;
`a_n=-2+(n-1)(-5)`

Explanation:

Arithmetic sequence states that a sequence where the difference between each successive pair of terms is the same.

The general rule for the arithmetic sequence is given by;

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

a represents the first term

d represents the common difference and

n represents the number of terms.

Given:
`a_3 = -12` and
`a_8 = -37`

`a_3 = -12`

a+(3-1)d = -12 [Using arithmetic sequence rule]

a + 2d = -12

or we can write this as;

a = -12 - 2d ......[1]

Similarly, for
`a_8 = -37` we have;

`a+(8-1)d = -37`

a+7d = -37 ......[2]

Substitute equation [1] into [2] to solve for d;

-12 - 2d +7d = -37

Combine like terms;

-12 + 5d = -37

Add both sides 12 we get;

-12 + 5d + 12 = -37 + 12

Simplify:

5d = -25

Divide both sides by 5 we get;

d = -5

Substitute the value of d in equation [1] to solve for a;

a = -2(-5) - 12

a = 10 -12 = -2

∴ a = -2

therefore, the general rule for the arithmetic sequence with
`a_3 = -12` and
`a_8 = -37` is,
`a_n=-2+(n-1)(-5)`