Sequence

It is given that the common difference of an arithmetic sequence is -5/2and the 9th term is 11. Find
(a) the general term T(n) ofthe sequence.
(b) the first negative term ofthe sequence.

(a)
For the arithmetic sequence:
T(1) = a
d = -5/2

The 9th term:
a + (9 - 1)d = 11
a + 8(-5/2) = 11
a - 20 = 11
a = 31

T(n) = 31 + (n - 1)(-5/2)
T(n) = (62 - 5n + 5)/2
T(n) = (67 - 5n)/2

(b)
When T(n) < 0
(67 - 5n)/2 < 0
67 - 5n < 0
5n > 67
n > (13 and 2/5)

Since n is an integer, thus n = 14

The first negative term
= (67 - 5*14)/2
= -3/2


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In a flower bed, the flowers are plated in thefollowing way:
In each row, there are 4 flowers lessthan that in the preceding row.
If there are 145 flowers inthe 1st row,
(a) express the number of flowers in the nth row in terms of n.
(b) which row has 61 flowers?

(a)
The number of flowers in the nth row is an arithmetic sequence.
T(1) = a = 145
d = -4

The number of flowers in the nth row, T(n)
= a + (n - 1)d
= 145 + (n - 1)(-4)
= 145 - 4n + 4
= 149 - 4n

(b)
For the row has 61 flowers:
149 - 4n = 65
4n = 84
n = 21
Hence, the 21st row has 61 flowers.

2011-08-29 12:31:41 補充：
Part (b) of Q(2) should be:

For the row has 61 flowers:
149 - 4n = 61
4n = 88
n = 22
Hence, the 22nd row has 61 flowers. ...... (answer)