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11 | P a g e

8. (a) The sum of the first six terms and the sixth term of an arithmetic sequence are S 6

and T respectively. If S  6 T  6 35, find the eleventh term of the sequence given
6

that the first term is 3.
 1  n 1
(b) The nth term of a sequence is given by T  3   .
n
 2 
(i) Show that the sequence is a geometric sequence.
(ii) Find the sum of the first six terms of this sequence.

x
1
9. (a) For the sequence 2,2 ,2 2x 1 ,2 3x 1 ,..., show that it is a geometric sequence.

(b) The second and the fifth terms of an arithmetic sequence are –12 and 324

respectively. Find the first term, a and the common difference, d.

10. The geometric sequence is given by 5, 25, 125,… .
(a) Find the first term and the common ratio.

(b) Find the nth term.
(c) Find the least number of terms so that the sum of this geometric sequence is exceed

20000.

11. Find the sum of the even numbers between 199 and 1999.

1
12. The sum of the first four terms of a geometric series with common ratio  is 30.
2

Determine the tenth term.

n
13. The sum of the first n terms of an arithmetic sequence is ( 4  20 ) .
n
2
1)
(a) Write down an expression for the sum of the first (n terms.
(b) Find the first term and the common difference of the above sequence.

1 1
14. The third and the sixth terms of a geometric series are and . Determine the values of
2 16
the first term and the common ratio. Hence, find the sum of the first nine terms of the series.