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## GRE - Quantitative Reasoning - Sequences and series

### In the sequence above, each term after the first term is equal to the preceding term plus the constant c (more)

a1, a2, a3 . . . an

In the sequence above, each term after the first term is equal to the preceding term plus the constant c. If a1  a3  a5 = 27 , what is the value of a2  a4 ?

The given sequence is an arithmetic sequence

thus,

ak = a1 + kc

a1 + a3 + a5 = 27

a1 + a1 + 2c + a1 + 4c = 27

3a1 + 6c = 27

a1 + 2c = 9

a2 + a4 = a1 + c + a1 + 3c = 2a1 + 4c = 2(a1 + 2c) = 2*9 = 18

### In the sequence a1, a2, a3,....a100, the kth term is defined as ak= 1/k - 1/k+1 for all integers k from 1 through 100. What is the sum of 100 terms of the sequence? (more)

In the sequence a1, a2, a3,....a100, the kth term is defined as ak= 1/k - 1/k 1 for all integers k from 1 through 100. What is the sum of 100 terms of the sequence?

A. 1/10100
B. 1/100
C. 1/101
D. 100/101
E. 1

ak = 1/k - 1/(k+1)

a1 = 1/1 - 1/2

a2 = 1/2 - 1/3

a3 = 1/3 - 1/4

.

.

a100 = 1/100 - 1/101