In an AP, the first term is 14, the last term is 104, and the number of terms is 19. What is the sum?
Answer and explanation
Correct answer: 1121
When the first term, last term, and number of terms are known, the most efficient AP formula is S_n = n/2(a + l), where a is the first term and l is the last term. Substituting n = 19, a = 14, and l = 104 gives S_19 = 19/2(14 + 104) = 19/2 × 118 = 19 × 59 = 1121. Therefore, option C is correct. There is no need to find the common difference or list all terms. The nearby options result from small arithmetic errors, such as mishandling 118/2 or multiplying 59 by an incorrect number.
Frequently asked questions
What is the correct answer to this question?
1121
Why is this the correct answer?
When the first term, last term, and number of terms are known, the most efficient AP formula is S_n = n/2(a + l), where a is the first term and l is the last term. Substituting n = 19, a = 14, and l = 104 gives S_19 = 19/2(14 + 104) = 19/2 × 118 = 19 × 59 = 1121. Therefore, option C is correct. There is no need to find the common difference or list all terms. The nearby options result from small arithmetic errors, such as mishandling 118/2 or multiplying 59 by an incorrect number.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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