If (S_{10}=250) and (S_9=207), what is the (10)th term?
Answer and explanation
Correct answer: 43
In an AP, the difference between the sums of the first n and first \(n-1\) terms gives the nth term: \(a_n=S_n-S_{n-1}\). Thus, \(a_{10}=S_{10}-S_9=250-207=43\). Therefore, 43 is correct. Getting 42 would mean subtracting the given sums incorrectly. Exam tip: When two consecutive partial sums are given, subtract them directly to obtain the corresponding term.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
In an AP, the difference between the sums of the first n and first \(n-1\) terms gives the nth term: \(a_n=S_n-S_{n-1}\). Thus, \(a_{10}=S_{10}-S_9=250-207=43\). Therefore, 43 is correct. Getting 42 would mean subtracting the given sums incorrectly. Exam tip: When two consecutive partial sums are given, subtract them directly to obtain the corresponding term.
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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