If an arithmetic progression has (S_4=44) and (S_9=189), what is the sum of the (5)th to (9)th terms?
Answer and explanation
Correct answer: (145)
The partial sum \\(S_4=44\\) contains the first four terms, while \\(S_9=189\\) contains the first nine terms. Subtracting the first sum from the second removes the common first four terms and leaves exactly the fifth, sixth, seventh, eighth, and ninth terms. Therefore, the required sum is \\(S_9-S_4=189-44=145\\).
This subtraction works for any sequence when partial sums are defined in the usual way, and it does not require finding the first term or common difference. Hence option C is correct. A value such as 140 could result from an arithmetic subtraction error, while adding the sums would count the first four terms twice and would not represent the requested block of terms.
Frequently asked questions
What is the correct answer to this question?
(145)
Why is this the correct answer?
The partial sum \\(S_4=44\\) contains the first four terms, while \\(S_9=189\\) contains the first nine terms. Subtracting the first sum from the second removes the common first four terms and leaves exactly the fifth, sixth, seventh, eighth, and ninth terms. Therefore, the required sum is \\(S_9-S_4=189-44=145\\).
This subtraction works for any sequence when partial sums are defined in the usual way, and it does not require finding the first term or common difference. Hence option C is correct. A value such as 140 could result from an arithmetic subtraction error, while adding the sums would count the first four terms twice and would not represent the requested block of terms.
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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