Problem Bank | IB Math AASL

[Maximum mark: 18]

Consider the sequence log2x,log2xa,log16x…, where a>0 and x>0,x=1.

First consider the case where the series is geometric.
1. Show that a=21.
  [4]
2. Given that S∞=−6, find the value of x.
  [3]
Next consider the case where the sequence is arithmetic.
1. Show that a=85
  [3]
2. Find d in the form d=qplog2x, where p,q∈Z.
  [1]
3. Given that the sum of the first n terms in the sequence is Sn=log2(√x51), find the value of n.
  [7]

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[Maximum mark: 18]

Consider the sequence log2x,log2xa,log16x…, where a>0 and x>0,x=1.

First consider the case where the series is geometric.
1. Show that a=21.
  [4]
2. Given that S∞=−6, find the value of x.
  [3]
Next consider the case where the sequence is arithmetic.
1. Show that a=85
  [3]
2. Find d in the form d=qplog2x, where p,q∈Z.
  [1]
3. Given that the sum of the first n terms in the sequence is Sn=log2(√x51), find the value of n.
  [7]

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

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