NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 55
Total: 106
Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
Solution:
Let the four numbers forming a G.P. be a, ar, a r 2 , a r 3
According to question,a r 2
⇒a ( r 2 – 1 ) a r 3 r 2
Dividing (i) by (ii), we get
Put r = – 2 in (i), we get a (4 – 1) = 9 ⇒ a =
Hence the four numbers forming a G.P. are 3, – 6, 12, – 24.
According to question,
⇒
Dividing (i) by (ii), we get
Put r = – 2 in (i), we get a (4 – 1) = 9 ⇒ a =
Hence the four numbers forming a G.P. are 3, – 6, 12, – 24.
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