If (a_2=14) and (a_8=50), what is the first term?
Answer and explanation
Correct answer: 8
In an arithmetic progression, the second term is
\(a_2=a+d=14\) and the eighth term is
\(a_8=a+7d=50\). Subtracting the equations gives
\(6d=36\), so
\(d=6\). Hence,
\(a=14-6=8\). Therefore, the first term is 8. Option 6 is the common difference, not the first term. Exam tip: when two terms are given, subtract their equations to find
\(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
In an arithmetic progression, the second term is
\(a_2=a+d=14\) and the eighth term is
\(a_8=a+7d=50\). Subtracting the equations gives
\(6d=36\), so
\(d=6\). Hence,
\(a=14-6=8\). Therefore, the first term is 8. Option 6 is the common difference, not the first term. Exam tip: when two terms are given, subtract their equations to find
\(d\) quickly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.
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