Sequences and Series · Question 3

For the functions f( )= 2 + 2 , and g( )= 2 + 2 , > >0, let 0< < 2 f( )= 0< < g( ). If the first term of a G.P. is ( 2 ), its common ratio is ( 2 ) and the sum of its first 10 terms is mn, (m, n)=1, then m+n is equal to .

Consider the quadratic equation (n2-2n+2 )x2-3x+ (n2-2n+2 )2=0, n R. Let be the minimum value of the product of its roots and be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is and the common ratio is , is :

1. 6137
2. 12181
3. 364243
4. 1093729

The sum 1+ 12 (12+22 )+ 13 (12+22+32 )+ upto 10 terms is equal to :

1. 130
2. 155
3. 3152
4. 3252

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

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

1. 65
2. 130
3. 220
4. 440

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

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

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

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

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