JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(\mathrm{a}\) and \(\mathrm{b}\) be be two distinct positive real numbers. Let \(11^{\text {th }}\) term of a \(GP\), whose first term is \(a\) and third term is \(b\), is equal to \(p^{\text {th }}\) term of another \(GP\), whose first term is \(a\) and fifth term is \(b\). Then \(\mathrm{p}\) is equal to
- A \(20\)
- B \(25\)
- C \(21\)
- D \(24\)
Answer & Solution
Correct Answer
(C) \(21\)
Step-by-step Solution
Detailed explanation
\( 1^{\text {st }} G P \Rightarrow t_1=a, t_3=b=a r^2 \Rightarrow r^2=\frac{b}{a} \) \( t_{11} =a r^{10}=a\left(r^2\right)^5=a \cdot\left(\frac{b}{a}\right)^5 \) \(2^{\text {nd }} \text { G.P. } \Rightarrow T_1=a, T_5=a r^4=b \)…
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