Arithmetic progression Trouble

[mark-ashleigh]

The first term of an arithmetic progression is (1-x)^2 and the second term is 1+x^2 .If the sumj of the first ten terms is 310 , find the possible values of x.

I have my A/S maths exam next month, but i am still having trouble with arithmetic progression. The above question is causing me some trouble .

First i expanded the brackets using binomial expansion .

Then as i had a quadratic i used the theorem to find values for x .

Once i found x i substituted into the first two terms to find the difference .

I found the first term = 1.98 the second = 6.8 with a diff of 4.8 .

As a + ( 9 X d ) = the tenth term = 45.36

And the formula for the sum is

S 10 = 10 x ( a + l)/2 ...where l = 45.36

Why do i keep getting 236 .7

Am i doing something drasticaly wrong?

Many thanks .

 

[arildno]

Do not double post in the future!

https://www.physicsforums.com/showthread.php?t=73728

 

[tacman]

It seems like you are on the right track with your approach to solving the problem. However, it's possible that you made a mistake in your calculations somewhere along the way. It's always a good idea to double check your work and make sure all of your calculations are accurate.

As for the value of 236.7, it's possible that you may have used the wrong formula for the sum. The formula you used, S10 = 10 x (a + l)/2, is the formula for the sum of an arithmetic series with an odd number of terms. Since we are dealing with 10 terms, which is an even number, we need to use a different formula: S10 = 10 x (2a + (n-1)d)/2.

Using this formula with the values you calculated for the first term, difference, and tenth term, we should get a sum of 310. So it's possible that the mistake lies in using the wrong formula.

In any case, it's important to carefully check your work and make sure all of your calculations are accurate. If you are still having trouble, don't hesitate to ask for help from your teacher or a tutor. With practice and patience, you will be able to master arithmetic progression and succeed on your exam. Good luck!