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Answer :
Final answer:
To find the nth term of an AP whose sum of r terms is given as 2r² + 3r, we subtract the sum of (n-1) terms from the sum of n terms, leading to the result that the nth term is n + 1.
Explanation:
The sum of r terms of an arithmetic progression (AP) is given by the formula 2r² + 3r. To find the nth term of this AP, we first need to find the sum of (n-1) terms, which is 2(n-1)² + 3(n-1). The nth term (an) can be found by subtracting the sum of the first (n-1) terms from the sum of the first n terms, which gives us the nth term as:
an = Sn - Sn-1 = [2n² + 3n] - [2(n-1)² + 3(n-1)]
Simplifying the above expression, we get:
an = (2n² + 3n) - (2n² - 4n + 2 + 3n - 3)
an = 2n² + 3n - 2n² + 4n - 2 - 3n + 3
Combining like terms, we find:
an = n + 1
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