Q84.The 4th term of GP is 500 and its common ratio is ๐โ๐. Let ๐๐ denote the sum of the first ๐ terms of ๐, ๐ is ______ this GP. If ๐6 > ๐5 + 1 and ๐7 < ๐6 + 12, then the number of possible values of
What This Question Tests
This question tests the understanding of geometric progression properties, particularly the nth term and sum of n terms. It involves setting up and solving inequalities to find possible integer values of the common ratio m.
Concepts Tested
Formulas Used
ar^(n-1)
Sn = a(r^n - 1)/(r - 1)
๐ NCERT Sections This Tests
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๐ Question Details
- Chapter
- Sequences & Series
- Topic
- Geometric Progression (GP)
- Year
- 2023
- Shift
- 24 Jan Shift 1
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
More from this Chapter
Q86.In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals (1) 1 2 (1 โโ5) (2) 21 โ5 (3) โ5 (4) 12 (โ5 โ1)
Q88.The sum of the series 2! 1 โ13! + 4!1 โโฆ upto infinity is (1) eโ2 (2) eโ1 (3) eโ1/2 (4) e1/2
Q71.Statement - 1: For every natural number n โฅ2, 1 + 1 + โฆ + 1 > โn. Statement โ2 : For every โ1 โ2 โn natural number n โฅ2, โn(n + 1) < n + 1. (1) Statement โ1 is false, Statement โ2 is true (2) Statement โ1 is true, Statement โ2 is true, Statement โ2 is a correct explanation for Statement โ1 (3) Statement โ1 is true, Statement โ2 is true; (4) Statement โ1 is true, Statement โ2 is false. Statement โ2 is not a correct explanation for Statement โ1.
Q76.The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is (1) โ4 (2) โ12 (3) 12 (4) 4