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15. The sum of the first k terms of an arithmetic series is 777. The first term is – 3 and the k-

th term is 77. Obtain the value of k and the eleventh term of the series.

n
16. The sum of the first n terms of an arithmetic series is (3n  5). If the second and the
2

fourth terms of the arithmetic series are the second and the third term of a geometric
series respectively, find the sum of the first eleven terms of this geometric series.

17. The fifth term and the tenth term of a geometric series are 3125 and 243 respectively. Find

the value of common ratio, r of the series.

th
18. The r terms of an arithmetic progression is (1 + 6r). Find in term of n, the sum of the first
n terms of the progression.

19. The first term and common difference of an arithmetic progression are a and –2

respectively. The sum of the first n terms is equal to the sum of the first 3n terms.
Express a in terms of n. Hence, show that n = 7 if a = 27.

20. The eighth and sixteenth terms of an arithmetic progression are 100 and 508 respectively.

Find the first term, the common difference and the sum of the first twenty terms.

21. The third term of an arithmetic series is 15. If the sixth term is half of the fourth term,

(a) determine the first five terms of the series.
(b) determine the sum of all the terms if given the last term is –126.

27
22. (a) The nth term of a sequence is T = n  13.Show that the sequence is an
n
2
arithmetic sequence.

(b) The second term of a geometric sequence is 12 and the fifth term is -96.
Determine the first term, a, and common ratio, r.