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Sequences and Series

JEE Main 2024 (Online) 29th January Morning ShiftMCQEasy📈 Topic in 40% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

  1. 7
  2. 6
  3. 5
  4. 4

Answer

(2) 6

Solution

Let the G.P. be a, ar, ar2, , ar63. The odd-placed terms a, ar2, , ar62 are 32 terms of a G.P. with common ratio r2.

Using the G.P. sum formula for both sums (r 1, since those values cannot satisfy the condition):

a(r64 - 1)r - 1 = 7 a(r64 - 1)r2 - 1

Since a(r64 - 1) 0, cancelling it gives r2 - 1 = 7(r - 1), i.e. r + 1 = 7.

∴ r = 6

Answer: (2)

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Ques. 2JEE Main 2024, 29 January (Evening Shift)

If e a, e b, e c are in an A.P. and e a- e 2b, e 2b- e 3c, e 3c- e a are also in an A.P., then a:b:c is equal to

  1. 6:3:2
  2. 9:6:4
  3. 25:10:4
  4. 16:4:1
Ques. 3JEE Main 2024, 29 January (Evening Shift)

If each term of a geometric progression a1, a2, a3, with a1= 18 and a2 a1, is the arithmetic mean of the next two terms and Sn=a1+a2+ +an, then S20-S18 is equal to

  1. -215
  2. 215
  3. -218
  4. 218
Ques. 4JEE Main 2024, 27 January (Morning Shift)

The number of common terms in the progressions 4, 9, 14, 19, , up to 25th term and 3, 6, 9, 12, , up to 37th term is :

  1. 9
  2. 8
  3. 5
  4. 7
Ques. 5JEE Main 2024, 27 January (Morning Shift)

If 8=3+ 14(3+p)+ 142(3+2p)+ 143(3+3p)+ , then the value of p is .

Ques. 6JEE Main 2024, 27 January (Evening Shift)

The 20th term from the end of the progression 20, 19 14, 18 12, 17 34, , -129 14 is :

  1. -115
  2. -100
  3. -110
  4. -118

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All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
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