Arithmetic progression Trouble

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SUMMARY

The discussion centers on solving an arithmetic progression problem where the first term is defined as (1-x)^2 and the second term as 1+x^2. The sum of the first ten terms is given as 310. The user correctly applies binomial expansion and quadratic theorem to find values for x, ultimately calculating the first term as 1.98 and the second term as 6.8, leading to a common difference of 4.8. However, the user encounters a discrepancy in the sum calculation, yielding 236.7 instead of the expected 310, indicating a miscalculation in the application of the sum formula.

PREREQUISITES
  • Understanding of arithmetic progression concepts
  • Familiarity with binomial expansion
  • Knowledge of quadratic equations and the quadratic formula
  • Ability to apply the sum formula for arithmetic series, S_n = n/2 * (a + l)
NEXT STEPS
  • Review the derivation and application of the arithmetic progression sum formula
  • Practice solving quadratic equations using the quadratic formula
  • Explore binomial expansion techniques in greater depth
  • Investigate common pitfalls in arithmetic progression calculations
USEFUL FOR

Students preparing for mathematics exams, particularly those studying arithmetic progressions, quadratic equations, and series summation techniques.

mark-ashleigh
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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 .
 
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