If the 4th term of an AP is 21 and d = 6, what is the 10th term?
Answer and explanation
Correct answer: 57
The governing concept is equal-step movement in an arithmetic progression. The tenth term is six positions after the fourth term because 10 − 4 = 6. Each step adds the common difference d = 6, so a_10 = a_4 + (10 − 4)d = 21 + 6 × 6 = 21 + 36 = 57. Therefore option C is correct. There is no need to calculate the first term, although the standard nth-term formula would give the same result after finding it. Option A, B, or D results from adding an incorrect number of differences or making an arithmetic error. Counting the gap between indices is especially useful when a middle term, rather than the first term, is supplied.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
The governing concept is equal-step movement in an arithmetic progression. The tenth term is six positions after the fourth term because 10 − 4 = 6. Each step adds the common difference d = 6, so a_10 = a_4 + (10 − 4)d = 21 + 6 × 6 = 21 + 36 = 57. Therefore option C is correct. There is no need to calculate the first term, although the standard nth-term formula would give the same result after finding it. Option A, B, or D results from adding an incorrect number of differences or making an arithmetic error. Counting the gap between indices is especially useful when a middle term, rather than the first term, is supplied.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term 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.
