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Answer :
Final answer:
Through the application of formulas for the sum and nth term of an arithmetic progression, the number of terms in the sequence, given the first and last terms and the sum, is found to be 8.
Explanation:
To find the number of terms in an arithmetic progression (AP) when the first and last terms are 1 and 11 respectively, and the sum of its terms is 36, we can use the formula for the sum of an AP: S = n/2 [2a + (n - 1)d], where S is the sum of the progression, n is the number of terms, a is the first term, and d is the common difference. Given that a = 1, S = 36, and the last term l = 11, we can also use the formula l = a + (n - 1)d to find d. Substituting the values into both equations, we find that n = 8.
This problem demonstrates the use of algebraic techniques to solve for unknowns in sequences and series, a key skill in high school mathematics.
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