The first difference of a sequence is the arithmetic sequence
2, 4, 6, 8, 10, Find the first six terms of the original sequence in each of the following cases.

a. The first term of the original sequence is 1
b. The sum of the first two terms in the original sequence is
10.
c. The fifth term in the original sequence is
36.

a). 1, 3, 5, 7, 9, 11

b). 4, 6, 8, 10, 12, 14

c). 28, 30, 32, 34, 36, 38

Step-by-step explanation:

Solution for question (a):

The first difference of a sequence is the arithmetic sequence;

2, 4, 6, 8, 10

As clearly shown, the common difference (d) is 2.

This sequence, above, is an arithmetic sequence.

If the first term of an arithmetic sequence (AP) is 1, then the first six terms would be:

1, 3, 5, 7, 9, 11

Solution for question (b):

If the sum of the first two terms of an AP is ten,

Lets say the first term is x and the second term is x + 2 then;

x + (x + 2) = 10

2x = 10 - 2

x = 4

So the first term is 4 and the six terms of the AP are:

4, 6, 8, 10, 12, 14

Solution for question (c):

If the fifth term of an AP is 36 then,

To find the nth term in an AP we use the formula;

 (where is the nth term, is the first term and is the common difference).

36 = a + (5 - 1)2

36 = a + 8

a = 36 - 8 = 28

So the first term is 28 and the first terms are;

28, 30, 32, 34, 36, 38

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step-by-step explanation: