# Construct an arithmetic sequenceÂ Construct an arithmetic sequence and find the first term if the common difference is 2 and the third term plus the fourth term = 8?

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### 2 Answers

As you have given a common difference we know that it is an AP.

If the 1st term of an AP is a and the common difference is d, the nth term is given as a + (n - 1)d

The third term is a + 2d and the fourth term is a + 3d

We have a + 2d + a + 3d = 8 and d = 2

=> 2a + 10 = 8

=> a = -1

**So the required series is -1, 1, 3, 5, 7...**

To create an arithmetic sequence, we'll have to know 2 basic terms: the 1st term and the common difference. The common difference is known but the 1st term is not known.

From enunciation we'll get the information that:

a3 + a4 = 8 (1)

By definition, the difference between 2 consecutive terms of an arithmetial progression is the common difference of the arithmetic sequence.

a4 - a3 = d

But, the common difference is d = 2, then:

a4 - a3 = 2 (2)

We'll add (1) + (2):

a3 + a4 - a3 + a4 = 8 + 2

We'll eliminate and combine like terms:

2a4 = 10

a4 = 10/2

a4 = 5

a3 = a4 - 2

a3 = 5 - 2

a3 = 3

But a3 = a1 + 2d

3 = a1 + 4

a1 = 3 - 4

a1 = -1

**The first term of the created arithmetic sequence, whose common difference is d=2, is a1 = -1.**