Question

Find the common difference of the arithmetic progression and write the next two terms for the sequence: 1.0,1/4,1/2,3/4.

a) Common difference: 1/4, Next term: 5/4, 3/2
b) Common difference: 1/4, Next term: 1/4, 1/2
c) Common difference: 1/2, Next term: 5/4, 3/2
d) Common difference: 1/2, Next term: 1/4, 1/2

Answer 1

The common difference is -3/4. The next terms in the sequence are 0 and -3/4.

Step-by-step explanation:

The common difference for an arithmetic progression can be found by subtracting any two consecutive terms. In this case, we subtract the second term from the first term.

1/4 - 1.0 = -3/4

So, the common difference is -3/4.

The next term in the sequence can be found by adding the common difference to the last term.

3/4 + (-3/4) = 0

Therefore, the next term is 0.

To find the following term, we add the common difference to the last term again:

0 + (-3/4) = -3/4

Therefore, the second next term is -3/4.