What's the formula for the nth term of a arithmetic sequence if a4=-10 and a10=-25

Question

I need to know how to do it

Answer 1

Hi Ashely,

 

 

The formula for the nth term of an arithemetic sequence is

 

a_n  = a₁ + (n-1)d

 

where a₁ is the first term

 

and d = the common difference

 

in your problem we can find the common difference by dividing the

 

difference between -25 and -10 by 6  (there are six terms from the 4th to the 10th

 

so d = (-25 - (-10))/6

 

d = -15/6

 

d = -2.5

 

we can find the a₁ term  as follows

 

 

-10 = a₁ + (4-1) (-2.5)    (in this case we know the 4th term, and we know the difference find a₁

 

-10 = a₁ + -7.5

 

so a₁ = -2.5

 

and the formula to find the nth term would be

 

a_n =-2.5 + (n-1)(-2.5)

 

Hope this helps

Answer 2

To get the nth term of a sequence, you need to know one term (any one will do) and the difference between each term.

 

First find the difference.  If you know two terms, subtract the earlier term from the later term, and divide by the number of steps between them.  So in this case you know the 10th term and the 4th.  So subtract the 4th term from the 10th:

 

(-25) - (-10) = -15

 

...and then divide by 6, (4th to 10th is 6 steps).

 

-15/6 = -2.5 or -5/2.

 

Now the formula is:

 

A_n = A_k + (n - k) d

 

where...

 

A_n is the nth term

A_k is the term you know

d is the difference between terms

 

So in this case you'd have:

 

A_n = A₄ + (n - 4)(-5/2)

A_n = A₄ - (n - 4) 5/2

 

...or...

 

A_n = A₁₀ + (n - 10)(-5/2)

A_n = A₁₀ - (n - 10) 5/2

 

Answer 3