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Find the expression for the sum to (n-1) terms when sum of nth term of a series is Sn= 17n - 3n^2

ii find a and d

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Final answer:

The expression for the sum of (n-1) terms is 3n^2 - 15n - 17. The value of a is 5 and the value of d is -6.

Step-by-step explanation:

To find the expression for the sum of (n-1) terms, we can first find the expression for the sum of the first n terms (Sn). The given expression for Sn is 17n - 3n^2. To find the sum of (n-1) terms, we subtract the nth term from Sn.

So, the expression for the sum of (n-1) terms is: Sn - (17n - 3n^2) = 3n^2 -17n + 2n - 17 = 3n^2 - 15n - 17.

To find the values of a and d, we can compare the given expression of Sn=17n - 3n^2 to the general formula for the sum of an arithmetic series: Sn = (n/2)(2a + (n-1)d). By comparing the coefficients of n^2 and n, we can find the values of a and d.

From the given expression, the coefficient of n^2 is -3. So, we have -3 = (n/2)d. Solving for d, we get d = -6.

From the given expression, the coefficient of n is 17. So, we have 17 = 2a - d. Substituting the value of d we found earlier, we get 17 = 2a - (-6) = 2a + 6. Solving for a, we get a = 5.

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