If (a_9=70) and (d=3), what is the (15)th term?
Answer and explanation
Correct answer: (88)
In an arithmetic progression, moving from the ninth term to the fifteenth term means moving forward by six positions: from term 9 to terms 10, 11, 12, 13, 14, and 15. Each forward position increases the value by the common difference 3. Thus, the total increase is six times 3, and this increase is added to the known ninth term. This avoids finding the first term unnecessarily.
The calculation is \\(a_{15}=a_9+(15-9)d\\). Substituting the given values gives \\(a_{15}=70+6\\times3=70+18=88\\). Therefore, option C is correct. The number of steps is 6, not 15, because the known term is already the ninth term; only the distance between the term numbers matters.
Frequently asked questions
What is the correct answer to this question?
(88)
Why is this the correct answer?
In an arithmetic progression, moving from the ninth term to the fifteenth term means moving forward by six positions: from term 9 to terms 10, 11, 12, 13, 14, and 15. Each forward position increases the value by the common difference 3. Thus, the total increase is six times 3, and this increase is added to the known ninth term. This avoids finding the first term unnecessarily.
The calculation is \\(a_{15}=a_9+(15-9)d\\). Substituting the given values gives \\(a_{15}=70+6\\times3=70+18=88\\). Therefore, option C is correct. The number of steps is 6, not 15, because the known term is already the ninth term; only the distance between the term numbers matters.
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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