AQA Core 2 Sequences and series

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Section 2: Arithmetic sequence and series

Exercise

1. Write each of the following series in the form 1

n

r

r

u .

(i) 2 + 4 + 6 + . + 20 (ii) 1 + 4 + 9 + + 144

(iii) 1 1 1

1 ...2 3 20

(iv) 1 2 + 4 8 + + 64

2. Find

(i) 5

1

(2 1) r

(ii) 4

2

1

r

(iii) 4

0

2 r

3. Find the 15th

term of the arithmetic sequence

-12, -5, 2, 9,

4. An arithmetic sequence begins 1, 4, 7, 10, ... (i) Find the 20th term. (ii) The last term is 127. Find the number of terms in the sequence.

5. Find the sum of the first 50 odd numbers.

6. The first term of an arithmetic sequence is 2 and the common difference is 4. (i) Find the 8th term. (ii) Find the sum of the first 10 terms. (iii) The last term is 278. How many terms are there in the sequence?

7. An arithmetic sequence has 15 terms. The first term is 30 and the last term is 12. (i) Find the common difference. (ii) Find the sum of the terms of the sequence.

8. Find the sum of the series 2 + 5 + 8 + . + 92.

9. The 7th term of an arithmetic sequence is -2 and the 12th term is 8. (i) Find the first term and the common difference. (ii) The sum of the terms of the sequence is 364.

Find the number of terms in the sequence.

10. The kth term of an arithmetic sequence is given by 5k 3.

AQA C2 Sequences 2 Exercise

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(i) Write down the first three terms of the sequence, and find the common difference.

(ii) Find the sum of the first 20 terms of the sequence.

11. The sum of the first n terms of an arithmetic sequence is given by 24 2nS n n .

(i) Write down the first term. (ii) Find the second term and hence the common difference. (iii) Find an expression for the kth term of the sequence.

12. The first term of an arithmetic sequence is 120 and the common difference is 7. (i) For what value of k is the kth term first negative? (ii) For what value of n is the sum of the first n terms first negative?

13. Salim uses an exercise bike each time he goes to the gym. The first time he goes he uses the bike for 10 minutes. Each time he uses the bike he increases his time

by 2 minutes. He aims to eventually use the bike for 30 minutes.

(i) On which session does Salim use the bike for 30 minutes for the first time? (ii) After the session on which Salim first uses the bike for 30 minutes, for how

many minutes in total has he used the bike by this time?