Arithmetic sequences and seriesEdexcel International A Level Maths: Subtopic test

1. 1
   The first term of an arithmetic sequence is $7$ and the common difference is $4$.

   (a)

   Find the 20th term.

   [1 mark]

   • A$83$
   • B$87$
   • C$80$
   • D$76$

   (b)

   Find the sum of the first 20 terms.

   [1 mark]

   • A$1800$
   • B$940$
   • C$900$
   • D$830$

   (c)

   Find the smallest value of $n$ for which the $n$th term is greater than $200$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sequence has $r$th term $u_r=3r+1$.

   (a)

   Find the value of $\displaystyle\sum_{r=1}^{10}u_r$.

   [1 mark]

   • A$165$
   • B$350$
   • C$31$
   • D$175$

   (b)

   Which expression gives $\displaystyle\sum_{r=1}^{n}u_r$?

   [1 mark]

   • A$\frac{n(3n+1)}{2}$
   • B$\frac{n(3n+5)}{2}$
   • C$\frac{n(3n+8)}{2}$
   • D$n(3n+5)$

   (c)

   Find the value of $\displaystyle\sum_{r=11}^{20}u_r$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An arithmetic series has third term $11$ and eighth term $36$. The sum of the first $n$ terms is $S_n$.

   (a)

   Find the first term and the common difference.

   [3 marks]

   (b)

   Find the smallest value of $n$ for which $S_n>1000$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An arithmetic series has first term $a$ and common difference $d$. The $n$th term is $u_n$ and the sum of the first $n$ terms is $S_n$.

   (a)

   Prove that $S_n=\frac n2\left[2a+(n-1)d\right]$.

   [6 marks]

   (b)

   Given that $u_5=17$ and $S_{12}=258$, find $a$ and $d$, and hence find the value of $n$ for which $S_n=670$.

   [6 marks]

   Total for question 4: 12 marks

End of questions