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A) Write the sequence of natural numbers which are multiplied by 3 ?

b) Write the sequence of natural numbers which are multiplied by 3 and added to 1 ?
c) Check whether the sequence obtained above is an arithmetic sequence or not?​

1 Answer

1 vote

Answer:

a) 3, 6, 9, 12, 15,...,
3\cdot n, b) 4, 7, 10, 13, 16,...,
3\cdot n +1, c) Both sequences are arithmetic.

Explanation:

a) The sequence of natural numbers which are multiplied by 3 are represented by the function
f(n) = 3\cdot n,
n\in \mathbb{N}. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...

b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function
f(n) = 3\cdot n + 1,
n\in \mathbb{N}. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...

c) Both sequences since differences between consecutive elements is constant. Let prove this statement:

(i)
f(n) = 3\cdot n


\Delta f = f(n+1) -f(n)


\Delta f = 3\cdot (n+1) -3\cdot n


\Delta f = 3

(ii)
f(n) = 3\cdot n +1


\Delta f = f(n+1)-f(n)


\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)


\Delta f = 3

Both sequences are arithmetic.

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