The sequence \( \left\langle a_{n-1}\right\rangle, n \in N \) is an...

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The sequence \( \left\langle a_{n-1}\right\rangle, n \in N \) is an arithmetical progression and \( d \) is its common
P difference. If \( \lim _{n \rightarrow \infty}\left(1-\frac{d^{2}}{a_{1}^{2}}\right)\left(1-\frac{d^{2}}{a_{2}^{2}}\right) \ldots\left(1-\frac{d^{2}}{a_{n}^{2}}\right) \) converges to \( \frac{1}{4} \) and \( a_{1}=8 \), then find

W the value of \( d \).
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