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?

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 \(k\log 2\)

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

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.

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?

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

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

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.

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

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?

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

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

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

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.

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

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

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?