In an arithmetic progression, a = 25 and d = −2. What is the sum of the first 20 terms?
Answer and explanation
Correct answer: 120
The governing AP sum formula is S_n = n/2[2a + (n − 1)d]. Here n = 20, a = 25, and d = −2. Substitution gives S_20 = 20/2[2(25) + 19(−2)] = 10[50 − 38] = 10×12 = 120. Thus option C is correct. The negative common difference means the terms decrease: 25, 23, 21, and so on, so the bracket must contain 50 − 38 rather than 50 + 38. The values 100, 110, and 130 can result from mishandling the negative sign or using the wrong number of difference intervals.
Frequently asked questions
What is the correct answer to this question?
120
Why is this the correct answer?
The governing AP sum formula is S_n = n/2[2a + (n − 1)d]. Here n = 20, a = 25, and d = −2. Substitution gives S_20 = 20/2[2(25) + 19(−2)] = 10[50 − 38] = 10×12 = 120. Thus option C is correct. The negative common difference means the terms decrease: 25, 23, 21, and so on, so the bracket must contain 50 − 38 rather than 50 + 38. The values 100, 110, and 130 can result from mishandling the negative sign or using the wrong number of difference intervals.
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.
