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থিম নির্বাচন

আপনার পছন্দের থিম বেছে নিন।

In the sequence an, the n-th term is defined as \(a_{n}=\left(a_{n-1}-1\right)^{2}\). If \(a_{3}=64\), then what is the vale of \(a_{1}\)?

A. 1
B. 3
C. 4
D. 9
E. none of these
Explanation: \(a_{3}=\left(a_{2}-1\right)^{2} \Rightarrow 64=a_{2}-1 \Rightarrow a_{2}=9\). একইভাবে, \(a_{2}=\left(a_{1}-1\right)^{2} \Rightarrow 9=\left(a_{1}-1\right)^{2} \Rightarrow a_{1}=4\) or \(a_{1}=-2\). Since the terms are squares, \(a_{1}\) must be a positive integer, so \(a_{1}=4\).