, ARITHMETIC SEQUENCES linear
An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive
terms is constant .
a represents Ti
Eg 5,7 . ,
9 , 11,13 ,
15 . . .
n position of the term
d represents the common difference
The term ( nth term / Tn ) be represented by In (n 1) d
general
=
can a + -
between terms .
d can be found by D= Tn Tn -
- i
3 3 5 5
^^
Eg Determine .
the 21ˢᵗ term of the AP 10 ; 13:16 Eg Determine
.
which term of -9 ;^_ 4%1 = 46
i. D= 13 -10 =3 •
find common difference i. D= -4-9=5
i. Tn -
_ at Cn 1) d -
: Tn = a + (n - 1) d
Tn = to + ( n 1) 3 -
'
substitute terms Tn = -9 + ( n 1) 5-
Tn = 10 -13N -3 Tn
'
=
Sn -
14
^
find equation
:
3. n -17 46 Sn
'
in 14 make equation 46
_
= = - =
find nth (21) term find term
" -
Tzi =3 ( 21 ] -17
'
n =
12
:
=
70 1-12=46
Eg . Determine the first term of the arithmetic sequence in which the 10th term is 31 and the 43rd is 130
i. Tn = a + Cn 1) d
-
: 130 = ( 31 -9 d) + 42nd - : 31
-
9C 3) = a
>
,,,o=a,,,a✓
Tio
=
at Clo -
1) d 99=33 d 4=9
→
=
"
Tio at 9d 1-43 =
a -142 d 3 =D
,
,, , g , ga
31 -
9d=a
" "
Generally when given information about terms , the gaps between the terms will be the same a+Cn 1) d
-
Ti T2 T] T>
a aid and at Gd Eg .
In an Ap th 3ʳᵈ term is -4 and the 7ᵗʰ is -20 ,
Determine
. . .
,
a- v. first 4 terms
3
'
a+2d=-4 2 at Gd =
-20 -
4- 2d -16cL = -20 4 a = -4 - 2C -
4) 5 4; 6; -4 ; -8
9=-4 -
2d -4+41=-20 9=4
D= -4
An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive
terms is constant .
a represents Ti
Eg 5,7 . ,
9 , 11,13 ,
15 . . .
n position of the term
d represents the common difference
The term ( nth term / Tn ) be represented by In (n 1) d
general
=
can a + -
between terms .
d can be found by D= Tn Tn -
- i
3 3 5 5
^^
Eg Determine .
the 21ˢᵗ term of the AP 10 ; 13:16 Eg Determine
.
which term of -9 ;^_ 4%1 = 46
i. D= 13 -10 =3 •
find common difference i. D= -4-9=5
i. Tn -
_ at Cn 1) d -
: Tn = a + (n - 1) d
Tn = to + ( n 1) 3 -
'
substitute terms Tn = -9 + ( n 1) 5-
Tn = 10 -13N -3 Tn
'
=
Sn -
14
^
find equation
:
3. n -17 46 Sn
'
in 14 make equation 46
_
= = - =
find nth (21) term find term
" -
Tzi =3 ( 21 ] -17
'
n =
12
:
=
70 1-12=46
Eg . Determine the first term of the arithmetic sequence in which the 10th term is 31 and the 43rd is 130
i. Tn = a + Cn 1) d
-
: 130 = ( 31 -9 d) + 42nd - : 31
-
9C 3) = a
>
,,,o=a,,,a✓
Tio
=
at Clo -
1) d 99=33 d 4=9
→
=
"
Tio at 9d 1-43 =
a -142 d 3 =D
,
,, , g , ga
31 -
9d=a
" "
Generally when given information about terms , the gaps between the terms will be the same a+Cn 1) d
-
Ti T2 T] T>
a aid and at Gd Eg .
In an Ap th 3ʳᵈ term is -4 and the 7ᵗʰ is -20 ,
Determine
. . .
,
a- v. first 4 terms
3
'
a+2d=-4 2 at Gd =
-20 -
4- 2d -16cL = -20 4 a = -4 - 2C -
4) 5 4; 6; -4 ; -8
9=-4 -
2d -4+41=-20 9=4
D= -4
