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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 35 of 106
Marks: +1, -0
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
Solution:  
We have a8a_8 = 192, r = 2
∴ a8a_8 = ar7ar^7 ⇒ a(2)7a(2)^7 = 192 ⇒ a = 19227\frac{192}{2^7} = 32\frac{3}{2}
Now, a12a_{12} = ar11ar^{11} = 32×211\frac{3}{2} \times 2^{11} = 3072
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