Question

Write the algebraic expressions of the following arithmetic sequences.
1) 5,8, 11, 14
2) 20, 15, 10, 5,
3) -13,-9,-5, -1,.
4) -4,-10,-16, -22,​
please answer

Answer 1

Answer:

1) 3n+2

2) 25-5n

3) 4n-17

4) 2-6n

Answer 2

Answer:

1) x, (x + 3), (x + 6), (x + 9)

2) x, (x - 5), (x - 10), (x -15)

3) x, (x + 4), (x + 8), (x + 12)

4) x, (x - 6), (x - 12), (x - 18), (x - 24)

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Step-by-step explanation:

Looking at each AS (Arithmetic Sequence):

1. In the first AS, by observing the 1st and 2nd terms, we can say that they  

have a common difference of (+3) ⇒ because (8 - 5 = 3)

Hence, if we take the 1st term as 'x', we can say that 2nd term is (x + 3) = 8

Similarly the 3rd terms becomes (x + 3 + 3 = x + 6) = 11

⇒ This is how we write the terms in Algebraic Expressions.

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So, follow the same steps in all the A.Sequences, and you will get that:

2. In 2nd AS, the first term is 20 and the 2nd terms is 15. Hence, the common difference = 15 - 20 = (-5)

So the terms become → x, (x - 5), (x - 10), (x -15)

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3. In the 3rd AS, the first term is (-13) and 2nd term is (-9). hence, the common difference = (-9 -(-13)) = +4

So, the terms become → x, (x + 4), (x + 8), (x + 12)

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4. In the 4th AS, the 1st term is (-4) and the 2nd term is (-10). Hence, the common difference is (-10) -(-4) = (-6)

So, the terms become → x, (x - 6), (x - 12), (x - 18), (x - 24)

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ALWAYS HAPPY TO HELP!