Arithmetic sequences and seriesEdexcel A-Level Maths: Subtopic test

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

   (a)

   Find the $30$th term.

   [1 mark]

   • A$127$
   • B$120$
   • C$123$
   • D$119$

   (b)

   Find the sum of the first $30$ terms.

   [1 mark]

   • A$1950$
   • B$3900$
   • C$1845$
   • D$1890$

   (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
   The sum of the first $10$ terms of an arithmetic series is $185$ and the sum of the first $20$ terms is $670$.

   (a)

   Find the common difference of the series.

   [1 mark]

   • A$2$
   • B$4$
   • C$5$
   • D$3$

   (b)

   Find the first term of the series.

   [1 mark]

   • A$10$
   • B$5$
   • C$8$
   • D$18.5$

   (c)

   Find the sum of the $11$th to the $20$th terms inclusive.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An arithmetic series has first term $a$ and common difference $d$.

   (a)

   Prove that the sum of the first $n$ terms is $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$.

   [3 marks]

   (b)

   Given that the $4$th term is $17$ and that the sum of the first $12$ terms is $324$, find $a$ and $d$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An arithmetic sequence has $n$th term $u_n=80-3n$.

   (a)

   (i) State the first term and the common difference.
   (ii) Find the number of positive terms in the sequence.
   (iii) Hence find the greatest value of $S_n$, the sum of the first $n$ terms.

   [6 marks]

   (b)

   Find the least value of $n$ for which $S_n<0$.

   [6 marks]

   Total for question 4: 12 marks

End of questions