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Financial Maths, 2ADV M1 EQ-Bank 5 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 EQ-Bank 10 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(By elimination:)`

`a < 0\ \ text{(eliminate C)}`

`r < -1\ \ \->\ text{successive terms change sign and increase exponentially.}`

`text{(eliminate A and D)}`

`=> B`

Financial Maths, 2ADV M1 EQ-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, where\ \ |\ r\ | < 1.`

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

`=> B`