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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 36 of 106
Marks: +1, -0
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2q^2 = ps.
Solution:  
We are given
a5a_5 = ar4ar^4 = p .... (i)
a8a_8 = ar7ar^7 = q .... (ii)
a11a_{11} = ar10ar^{10} = s .... (iii)
Now multiply (i) and (iii), we get
ps = a2r14a^2 r^{14} = (ar7)2(ar^7)^2 = q2q^2 [using (ii)]
⇒ q2q^2 = ps.
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