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Sequences and Series · Question 7

JEE Main 2026 (Online) 5th April Morning ShiftMCQEasy📈 Topic in 55% papers+4−1
1

Let the sum of the first n terms of an A.P. be 3n2+5n. Then the sum of squares of the first 10 terms of the A.P. is:

  1. 10220
  2. 12860
  3. 15220
  4. 19780

Answer

(3) 15220

Solution

an=Sn-Sn-1= (3n2+5n )- (3(n-1)2+5(n-1) )=6n+2

Check: a1=S1=8=6(1)+2

n=110an2= n=110(6n+2)2=36 n2+24 n+4 10

n=110n2= 10 11 216=385, n=110n=55

Sum =36 385+24 55+40

=13860+1320+40=15220

Answer: (3)

JEE Main 2026 (Online) 5th April Morning Shift

Keep practising — Sequences and Series

2

n=110 ( 528n(n+1)(n+2) ) is equal to:

  1. 65
  2. 130
  3. 220
  4. 440
JEE Main 2026 (Online) 5th April Morning Shift
3

If the sum of the first 10 terms of the series 11+14 4+ 21+24 4 + 31+34 4+ 41+44 4+ is mn, (m, n)=1, then m+n is equal to :

  1. 256
  2. 264
  3. 276
  4. 284
JEE Main 2026 (Online) 5th April Evening Shift
4

Let A1, A2, A3, , A39 be 39 arithmetic means between the numbers 59 and 159. Then the mean of A25, A28, A31 and A36 is equal to :

  1. 129
  2. 136
  3. 131.50
  4. 134
JEE Main 2026 (Online) 5th April Evening Shift
5

The first term of an A.P. of 30 non-negative terms is 103. If the sum of this A.P. is the cube of its last term, then its common difference is:

  1. 587
  2. 2583
  3. 1529
  4. 529
JEE Main 2026 (Online) 4th April Morning Shift
6

Let = 14+ 18+ 116+ and = 13+ 19+ 127+ . Then the value of (0.2) 5( )+(0.04) 5( ) is equal to :

  1. 4
  2. 5
  3. 8
  4. 25
JEE Main 2026 (Online) 4th April Evening Shift
7

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in A B, which are divisible by 3, is :

  1. 4
  2. 5
  3. 6
  4. 7
JEE Main 2026 (Online) 2nd April Morning Shift
8

If k=1n ak=6n3, then k=16 ( ak+1-ak36 )2 is equal to .

JEE Main 2026 (Online) 2nd April Morning Shift
9

Let a1, a2, a3, be an A.P. and g1=a1, g2, g3, be an increasing G.P. If a1=a2+g2=1 and a3+g3=4, then a10+g5 is equal to:

  1. 81
  2. 76
  3. 62
  4. 55
JEE Main 2026 (Online) 2nd April Evening Shift
10

The sum 131+ 13+231+3+ 13+23+331+3+5+ up to 8 terms, is :

  1. 70
  2. 71
  3. 72
  4. 73
JEE Main 2026 (Online) 2nd April Evening Shift
11

The value of k=1 (-1)k+1 ( k(k+1)k! ) is

  1. e/2
  2. e
  3. 2/e
  4. 1/e
JEE Main 2026 (Online) 28th January Morning Shift

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