About Arithetic Progression

For arithemetic sequence, the general or nth term is an = a1 + (n-1)d,
where a1 is 1st tem, d is commom difference

1. a)the commom difference = ( x-3 ) - (x-8) = 5

b) Define the general term an = a1 + (n-1)d
put a1 = x - 8 , d = 5
therefore, general term = (x-8) + (n-1)(5) = x - 8 + 5n -5 = x +5n - 13



c)the 11th term

from (b) the general term = x +5n - 13, put n = 11

therefore, the 11th term = x + 5(11) - 13 = x +42


2. Define the general term an = a1 + (n-1)d
put a1 = 2 , d = 8 - 2 = 6
therefore, general term an = 2 + (n-1)(6) = 6n - 4

a)the 10th term a10 = 6(10) - 4 = 56

b)the 20th term a20 = 6(20) - 4 = 116

c) The value of an arithmetic series consisting n terms is given by
Sn = n[2a1 + (n-1)d] /2
the 1st term = a1 = 2
the common difference = 8 - 2 = 6
therefore, Sn = n [2(2) + (n-1)6]/2 = n(3n-1)

the sum of the series from the 10th term to the 20th term
= S20 - S9
= (20)[3(20) - 1] - (9)[3(9) - 1]
= 1180 - 234
= 946


3. Define the value of an arithmetic series consisting n terms is given by
Sn = n[2a1 + (n-1)d] /2
the 1st term = a1 = 32
the common difference = 29 - 32 = -3
therefore, Sn = n [32(2) + (n-1)(-3)]/2 = n(67 -3n)/2

a) there are totally 10 layers, therefore, the no. of sticks in the pile S10
S10 = (10)[67 -3(10)]/2 = 185

b)the number of sticks used to make the fence
= the number of sticks of all 10 layers - the number of sticks of lower 4 layers
= S10 - S4
= {(10)[67 -3(10)]/2} - { (4)[67 -3(4)]/2}
= 185 - 110
= 75

a the (n+1)th TERM - the n th=commom difference就可以了b
b general= x+(-8+5(n-1))
c put n=11 into general term

a general term= 2+6(n-1) put n=10
b put n=20
c sum of series= (first term+last term)*number of terms/2
the sum of first 20 term -the sum of first 9 term