Sequences and Series

For positive integers n, if 4an = (n2 + 5n + 6 ) and Sn = k=1n ( 1ak ), then the value of 507S2025 is :

1. 540
2. 675
3. 1350
4. 135

The interior angles of a polygon with n sides are in an A.P. with common difference 6 . If the largest interior angle of the polygon is 219 , then n is equal to .

Let Sn= 12+ 16+ 112+ 120+ upto n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is 2026 S2025, then the absolute difference between 20th and 15th terms of the A.P. is

1. 20
2. 45
3. 90
4. 25

In an arithmetic progression, if S40=1030 and S12=57, then S30-S10 is equal to :

1. 525
2. 505
3. 510
4. 515

If 7=5+ 17(5+ )+ 172(5+2 )+ 173(5+3 )+ , then the value of is :

1. 17
2. 1
3. 67
4. 6

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

1. -120
2. -1200
3. -1080
4. -1020

The roots of the quadratic equation 3x2-px+q=0 are 10th and 11th terms of an arithmetic progression with common difference 32. If the sum of the first 11 terms of this arithmetic progression is 88, then q-2p is equal to .

Let a1,a2,a3, be a G.P. of increasing positive terms. If a1a5=28 and a2+a4=29, then a6 is equal to:

1. 812
2. 784
3. 628
4. 526

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

1. 23
2. 13
3. 1
4. 0

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

1. 8
2. 6
3. 4
4. 5