If (a_2=10) and (d=4), what is the (6)th term?
Answer and explanation
Correct answer: (26)
In an arithmetic progression, moving from the rth term to the nth term requires n-r equal steps, each of size d. Here the given term is a_2=10, the required term is a_6, and d=4. The number of steps is 6-2=4, so a_6=a_2+(6-2)d=10+4(4)=10+16=26. Therefore option C is correct. A common mistake is to add only three differences or to use six differences, which would produce distractors such as 22 or 34. The formula a_n=a_r+(n-r)d avoids that indexing error and uses the supplied second term directly.
Frequently asked questions
What is the correct answer to this question?
(26)
Why is this the correct answer?
In an arithmetic progression, moving from the rth term to the nth term requires n-r equal steps, each of size d. Here the given term is a_2=10, the required term is a_6, and d=4. The number of steps is 6-2=4, so a_6=a_2+(6-2)d=10+4(4)=10+16=26. Therefore option C is correct. A common mistake is to add only three differences or to use six differences, which would produce distractors such as 22 or 34. The formula a_n=a_r+(n-r)d avoids that indexing error and uses the supplied second term directly.
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.
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