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Financial Maths, 2ADV M1 SM-Bank 10 MC

The graph above shows the first six terms of a sequence.

This sequence could be

  1. an arithmetic sequence that sums to one.
  2. an arithmetic sequence with a common difference of one.
  3. a geometric sequence with an infinite sum of one.
  4. a geometric sequence with a common ratio of one. 
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`D`

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`text(Series is 1, 1, 1, …)`

`text(The only possibility within the choices)`

`text(is a geometric sequence where)\ \  r=1.`

`=> D`

Financial Maths, 2ADV M1 SM-Bank 13 MC

The first term of a geometric sequence is `a`, where `a < 0`.

The common ratio of this sequence, `r`, is such that `r < –1`.

Which one of the following graphs best shows the first `10` terms of this sequence?

A1

 

A2

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`B`

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`text(Using elimination)`

`a < 0. text(Cannot be C.)`

`r < -1. text(Successive terms change sign and)`

`text(increase exponentially.)`

`text(Cannot be A, D.)`

`=> B`

Financial Maths, 2ADV M1 SM-Bank 9 MC

The graph above shows consecutive terms of a sequence.

The sequence could be

  1. geometric with common ratio r, where r < 0
  2. geometric with common ratio r, where 0 < r < 1
  3. geometric with common ratio r, where r > 1
  4. arithmetic with common difference d, where d < 0
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`B`

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`text (As)\ \ n\ \ text (increases,) \ \ t_n →0.`

`:.\ text (Series is a GP with a limiting sum,)`

`text(i.e.)\ \ |\ r\ | < 1.`

`text (Only one choice satisfies these conditions.)`

`rArr B`