Sequences and Series

JEE Main 2024 (Online) 29th January Evening ShiftMCQEasy📈 Topic in 40% papers+4−1

Ques. 1JEE 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

-215
215
-218
218

Answer

(1) -215

Solution

Let an=arn-1, a= 18

2an=an+1+an+2 2=r+r2 (r+2)(r-1)=0

a2 a1, r 1 r=-2

S20-S18=a19+a20=ar18(1+r)

= 18 218 (-1)=-215

Answer: (1)

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Ques. 2JEE 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 :

Ques. 3JEE 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. 4JEE 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 :

-115
-100
-110
-118

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