Arithmetic and geometric sequencesIB MYP Maths Extended: Subtopic test

1. 1
   An arithmetic sequence has first term $u_1=7$ and common difference $d=4$.

   (a)

   Find the $20$th term of the sequence.

   [1 mark]

   • A$87$
   • B$83$
   • C$80$
   • D$79$

   (b)

   Which term of the sequence is equal to $103$?

   [1 mark]

   • AThe $25$th term
   • BThe $24$th term
   • CThe $26$th term
   • DThe $96$th term

   (c)

   Find the sum of the first $20$ terms.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A geometric sequence has first term $u_1=3$ and common ratio $r=2$.

   (a)

   Find the $6$th term of the sequence.

   [1 mark]

   • A$192$
   • B$36$
   • C$48$
   • D$96$

   (b)

   Find the sum of the first $6$ terms of the sequence.

   [1 mark]

   • A$192$
   • B$93$
   • C$189$
   • D$381$

   (c)

   Find the position of the first term in the sequence that is greater than $1000$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Amira invests AED $2000$ in an account that pays $4\%$ compound interest per year. The interest is added at the end of each year. A calculator may be used.

   (a)

   Find the value of the investment after $5$ years, to the nearest fils (2 decimal places).

   [3 marks]

   (b)

   Find the number of whole years after which the investment is first worth more than AED $3000$. Show the values that support your answer.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Kwame compares two savings plans for the first $12$ months. In Plan A he saves AED $50$ in month $1$, and then AED $15$ more each month than in the previous month. In Plan B he saves AED $50$ in month $1$, and then $20\%$ more each month than in the previous month. A calculator may be used.

   (a)

   For Plan A, (i) find a formula for the amount $u_n$ saved in month $n$, (ii) find the total amount saved in the $12$ months, (iii) find the first month in which he saves more than AED $200$.

   [6 marks]

   (b)

   For Plan B, (i) find the amount saved in month $12$, (ii) find the total amount saved in the $12$ months. (iii) Kwame can afford to save at most AED $250$ in any one month. Evaluate whether Plan B or Plan A is better for him, justifying your answer.

   [6 marks]

   Total for question 4: 12 marks

End of questions