If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?
Answer and explanation
Correct answer: (34)
In an arithmetic progression, moving from the rth term to the nth term requires n−r equal steps, each of size d. The third term is given as 14, and the seventh term is four positions later. Therefore we do not need to find the first term; we can move forward by four common differences directly.
The number of steps is 7−3=4. Since d=5, the increase is 4×5=20. Thus the seventh term is \\(a_7=a_3+(7-3)d=14+4(5)=14+20=34\\). Hence the correct choice is C. Adding only three differences would reach the sixth term, while adding seven differences would ignore that the given value is already the third term.
Frequently asked questions
What is the correct answer to this question?
(34)
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. The third term is given as 14, and the seventh term is four positions later. Therefore we do not need to find the first term; we can move forward by four common differences directly.
The number of steps is 7−3=4. Since d=5, the increase is 4×5=20. Thus the seventh term is \\(a_7=a_3+(7-3)d=14+4(5)=14+20=34\\). Hence the correct choice is C. Adding only three differences would reach the sixth term, while adding seven differences would ignore that the given value is already the third term.
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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