Sequences and Series

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

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

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

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

1. 70
2. 71
3. 72
4. 73

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

1. e/2
2. e
3. 2/e
4. 1/e

The common difference of the A.P.: a1, a2, , am is 13 more than the common difference of the A.P.: b1, b2, , bn. If b31 = -277, b43 = -385 and a78 = 327, then a1 is equal to

1. 21
2. 19
3. 24
4. 16

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .

6326 + 10 1325 + 10 2324 + 10 22323 + + 10 2243 is equal to :

1. 226
2. 325
3. 326
4. 225