Summing an AP - Questions - Class Mathematics School Portal

Summing an AP - Questions

Question 1

51957

In an arithmetic progression, the sum of the first six terms is $78$ and the sum of the first ten terms is $210$. Find

i) The common difference

ii) The first term

Answer

i) $d=4$

ii) $a=3$

Worked Solution

Question 2

124472

In a card competition the first prize is $\$ 100$, the second prize is $\$ 90$, the third prize is $\$ 80$ and so on.

(i) Write down the value of the $n$th prize.

(ii) If the total prize money is $\$ 550$ how many prizes will there be?

Answer

i) $T_n=110-10 n$

ii) $1$

Worked Solution

Question 3

11987

Find the sum of the first 20 terms of the arithmetic series 2 + 5 + 8 + ...

Answer

610

Worked Solution

Question 4

11988

The first three terms of an arithmetic sequence are 29, 25, 21. What is the least number of terms to make the sum negative?

Answer

$n = 16$

Worked Solution

Question 5

12102

The first term of an A.P. is -3 and the 10th term is 24. The sum of the first 10 terms is?

Answer

105

Worked Solution

Question 6

12103

The sum of the 2nd and 4th term of an A.P. is 15 and the sum of the 5th and 6th term is 25. Find the first term.

Answer

$a = 3.5$

Worked Solution

Question 7

12104

The 4th term of an A.P. is 15 and the sum of the first 5 terms is 55. The common difference is?

Answer

$d = 4$

Worked Solution

Question 8

12105

The number of terms of $15+13+11+ ...$ required to make a total of $- 36$ is?

Answer

$n = 18$

Worked Solution

Question 9

12106

In an A.P., the sum of the first 5 terms is 30, and the 3rd term is equal to the sum of the first two terms. The common difference is?

Answer

$d = 2$

Worked Solution

Question 10

31053

The fifth term of an arithmetic sequence is 44, and the tenth term is 64.

(i) Find the value of the first term and the common difference.

(ii) Find the sum of the first 100 terms.

Answer

i) $28$ ii) $22,600$

Worked Solution

Question 11

31045

The sum to $n$ terms of an arithmetic sequence is given by $S_n = 2n^2 + 3n$. Find

i) the first term.

ii) the common difference.

iii) the number of terms required to give a sum of 1325.

Answer

i) $5$ ii) $4$ iii) $25$

Worked Solution

Question 12

31054

A company plans to sell 400 computers in its first month of operation. They plan to increase their sales by 40 computers each month. How many computers do they plan to sell,

i) in the last month of the first year of operation?

ii) over the entire 12 months?

Answer

i) $840$ ii) $7440 $

Worked Solution

Question 13

31043

The sum of the first 5 terms of an arithmetic series is 45, the sum of the first 10 terms is 145. Find

i) the common difference

ii) the first term

Answer

i) $2.2$ ii) $4.6$

Worked Solution

Question 14

31044

The sixth term of an arithmetic progression is 18 and the eleventh term is 24.

i) Find the common difference

ii) Find the sum of the first 20 terms

Answer

i) $1.2$ ii) $468$

Worked Solution

Question 15

24667

The sum of the first 5 terms of an arithmetic series is 45, the sum of the first 10 terms is 145. Find

(i) the common difference

(ii) the first term

Answer

(i) $d = 2.2$

(ii) The first term is 4.6.

Worked Solution

Question 16

24668

The first three terms of an arithmetic progression are 27, 23, 19

(i) Write down the sum of the first n terms of this series.

(ii) What is the least n such that the sum of the first n terms of the series is negative?

Answer

(i) $n(29 - 2n)$

(ii) $n = 15$

Worked Solution

Question 17

24669

For the first three terms of the series log 2, log 4, log 8 find

(i) The 6th term

(ii) The sum of the first six terms. Give your answer in the form $k\log 2$

Answer

(i) ${T_6} = 6\log 2$

(ii) $21\log 2$

Worked Solution

Question 18

24670

The sum of the first three terms of an arithmetic progression is 33 and the sum of the next three terms is 87

(i) Find the first term

(ii) Find the common difference

Answer

(i) $a = 5$

(ii) $d = 6$

Worked Solution