If the sum of the first n terms of an arithmetic progression is S_n = 5n² + 4n, what is the 18th term?
Answer and explanation
Correct answer: 179
The governing concept is that the nth term of an arithmetic progression can be obtained by subtracting consecutive partial sums: a_n = S_n − S_(n−1). First calculate S_18 = 5(18²) + 4(18) = 5(324) + 72 = 1692. Next calculate S_17 = 5(17²) + 4(17) = 5(289) + 68 = 1513. Therefore a_18 = S_18 − S_17 = 1692 − 1513 = 179. Hence option C is correct. The other values result from an arithmetic or substitution error, such as using the wrong preceding sum or confusing S_18, which is the total of the first 18 terms, with the 18th term itself.
Frequently asked questions
What is the correct answer to this question?
179
Why is this the correct answer?
The governing concept is that the nth term of an arithmetic progression can be obtained by subtracting consecutive partial sums: a_n = S_n − S_(n−1). First calculate S_18 = 5(18²) + 4(18) = 5(324) + 72 = 1692. Next calculate S_17 = 5(17²) + 4(17) = 5(289) + 68 = 1513. Therefore a_18 = S_18 − S_17 = 1692 − 1513 = 179. Hence option C is correct. The other values result from an arithmetic or substitution error, such as using the wrong preceding sum or confusing S_18, which is the total of the first 18 terms, with the 18th term itself.
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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