SOLUTION: Please can you help me with this. I've been trying but I can't seem to solve it. If the sum of the 8th and 9th terms of an a.p is 72 and the 4th term is -6, find the common diff

Algebra ->  Sequences-and-series -> SOLUTION: Please can you help me with this. I've been trying but I can't seem to solve it. If the sum of the 8th and 9th terms of an a.p is 72 and the 4th term is -6, find the common diff      Log On


   

Question 961982: Please can you help me with this. I've been trying but I can't seem to solve it.
If the sum of the 8th and 9th terms of an a.p is 72 and the 4th term is -6, find the common difference.
Thank you so much in advance.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this is an interesting problem.
i solve it this way.

the general equation is An = A1 + (n-1)*d

from this you get:

A4 = A1 + 3d
A8 = A1 + 7d
A9 = A1 + 8d

you are given that A4 is equal to -6.
from that you get:

-6 = A1 + 3d

you are given that the sum of A7 and A8 is equal to 72.
from that you get:

72 = A1 + 7d + A1 + 8d
combine like terms and you get:

72 = 2A1 + 15d

you now have two equations that need to be solved simultaneously.

they are:

-6 = A1 + 3d
72 = 2A1 + 15d

multiply the first equation by 2 and you get:

-12 = 2A1 + 6d
72 = 2A1 + 15d

subtract the first equation from the second equation and you get:

84 = 9d

solve for d and you get:

d = 9.333333333333333........ which is the same as (9 and 1/3).

that's your common difference.

you can confirm by using that value of d to solve for A1.
you will get A1 = -34.

you can then use A1 and d to solve for A4 and A8 and A9

you will find that A4 will be equal to -6 and the sum of A8 and A9 will be equal to 72.