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m + b, 2m + b, 3m + b, 4m + b, ... is an infinite sequence. This sequence may be defined in many ways. Which is not a correct way to define this sequence?

A) f(x) = mx + b for x = {1, 2, 3, ...}

B) f(x) = 2m + b + m(x − 2) for x = {1, 2, 3, ...}

C) an = m − b + m(n − 1) for n = {1, 2, 3, ...}

D) a1 = m + b and an + 1 = an + m for n = {1, 2, 3, ...}

Question

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rani01654 rani01654 · Answer 1 · 2020-01-20T11:16:17+01:00

Answer:

Option C is incorrect.

Step-by-step explanation:

An infinite series is given by m + b, 2m + b, 3m + b, 4m + b, ... .

A) The above sequence is given by f(x) = mx + b for x = {1, 2, 3, ......}

For, x = 1, f(x) = m + b

For, x = 2, f(x) = 2m + b

.............

So, this is a valid definition of the above sequence.

B) The above sequence is given by f(x) = 2m + b + m(x - 2) for x = {1, 2, 3, ......}

For, x = 1, f(x) = 2m + b - m = m + b

For, x = 2, f(x) = 2m + b + 0 = 2m + b

.............

So, this is a valid definition of the above sequence.

C) The above sequence is given by [tex]a_{n} = m - b + m(n - 1)[/tex] for n = {1, 2, 3, ......}

For, n = 1, [tex]a_{1} = m - b + m(1 - 1) = m - b[/tex]

For, n = 2, [tex]a_{2} = m - b + m(2 - 1) = 2m - b[/tex]

.............

So, this is not a valid definition of the above sequence.

D) The above sequence is given by[tex]a_{1} = m + b[/tex] and [tex]a_{n + 1} = a_{n} + m[/tex] for n = {1, 2, 3, .........}

For, n = 1, [tex]a_{1} = m + b[/tex]

For, n = 2, [tex]a_{2} = a_{1} + m = (m + b) + m = 2m + b[/tex]

.............

So, this is a valid definition of the above sequence.

Therefore, option C is incorrect. (Answer)