If the sum of the first (n) terms of an arithmetic progression is (S_n=4n^2+3n), what is the (25)th term?
Answer and explanation
Correct answer: 199
To find the nth term from the sum, use \(a_n=S_n-S_{n-1}\). Thus, \(a_n=(4n^2+3n)-[4(n-1)^2+3(n-1)]=8n-1\). Hence, \(a_{25}=8\times25-1=199\). The value 203 usually results from an error while subtracting or expanding the \((n-1)\) expression. Exam tip: when \(S_n\) is given, subtract consecutive sums to obtain a term.
Frequently asked questions
What is the correct answer to this question?
199
Why is this the correct answer?
To find the nth term from the sum, use \(a_n=S_n-S_{n-1}\). Thus, \(a_n=(4n^2+3n)-[4(n-1)^2+3(n-1)]=8n-1\). Hence, \(a_{25}=8\times25-1=199\). The value 203 usually results from an error while subtracting or expanding the \((n-1)\) expression. Exam tip: when \(S_n\) is given, subtract consecutive sums to obtain a 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
