Question
Download Solution PDFThe fifth term and the eighth term of a geometric progression are 27 and 729 respectively. What is its 11th term?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The fifth term of a geometric progression (GP) = 27
The eighth term of the GP = 729
Formula used:
General term of GP: Tn = a × rn-1
Where, a = first term, r = common ratio, n = term number
Calculation:
Fifth term: T5 = a × r4 = 27
Eighth term: T8 = a × r7 = 729
Dividing both equations:
⇒ (a × r7) / (a × r4) = 729 / 27
⇒ r3 = 27
⇒ r = 3
Substitute r = 3 into T5:
⇒ a × 34 = 27
⇒ a × 81 = 27
⇒ a = 27 / 81 = 1/3
T11 = (1/3) × 310
⇒ T11 = (1/3) × 59049
⇒ T11 = 19683
∴ The correct answer is option (1).
Last updated on Feb 11, 2025
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