MHT CET · Maths · Sequences and Series
For a sequence \(\left(t_{n}\right)\) if \(s_{n}=7\left(3^{n}-1\right)\), then \(t_{n}=\)
- A \((7) 3^{n-1}\)
- B (14) \(3^{n+1}\)
- C \((14) 3^{n-1}\)
- D \(\quad(7) 3^{n+1}\)
Answer & Solution
Correct Answer
(C) \((14) 3^{n-1}\)
Step-by-step Solution
Detailed explanation
A sequence; \(t_{n} ;\)
\(s_{n} =7\left(3^{n-1}\right) \)
\( s_{n-1} =7\left(3^{n-1}-1\right)\)
\(t_{n} =s_{n}-s_{n-1} \)
\( t_{n} =7\left(3^{n}-3^{n-1}\right) \)
\( =7 \cdot 3^{n-1} \cdot 2 \)
\( =14 \cdot 3^{n-1}\)
\(s_{n} =7\left(3^{n-1}\right) \)
\( s_{n-1} =7\left(3^{n-1}-1\right)\)
\(t_{n} =s_{n}-s_{n-1} \)
\( t_{n} =7\left(3^{n}-3^{n-1}\right) \)
\( =7 \cdot 3^{n-1} \cdot 2 \)
\( =14 \cdot 3^{n-1}\)
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