F5 maths about A.P

[匿名]

2009-09-07 4:39 am

1.
if the 1st term and the 8th term of an arithmetic sequence are 10 and -11 respectively,find
a, the common difference
b, the 25th term

2.
the sum of the 4th term and the 5th term of an arithmetic sequence is 18, if the sum of the first two terms is 42, find
a, the general term
b, the 15 th term

3.
write down the arithmetic sequence in each of the following
a, insert 6 numbers between the two numbers 34 and 97 and make the eight numbers an arithmetic sequence
b, insert 9 numbers between the two numbers 15 and 75 and make the eleven numbers an arithmetic sequence

回答 (1)

Prof. Physics

2009-09-07 5:27 am

✔ 最佳答案

1. 1st term, a = 10

Let d be the common difference

the 8th term, a + (8 - 1)d = -11

10 + 7d = -11

d = -3

b. The 25th term = a + (n - 1)d

= 10 + (25 - 1)(-3)

= -62

2.a. Let a and d be the 1st term and common difference respectively.

Sum of the first two terms, a + (a + d) = 42

2a + d = 42 ... (1)

Sum of the 4th and 5th term, [a + (4 - 1)d] + [a + (5 - 1)d] = 18

2a + 7d = 18 ... (2)

Solving (1) and (2), d = -4, a = 23

b. The 15th term = a + (n - 1)d

= 23 + (15 - 1)(-4) = -33

3.a. 97 - 34 = 63

63/7 = 9

So, the common difference should be 9.

So, the 8 numbers

= 34, 43, 52, 61, 70, 79, 88, 97

b. 75 - 15 = 60

60/10 = 6

So, the 11 numbers:

15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75

參考: Physics king

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