Arithmetic sequence

Arithmetic Sequence
if U1,U2,U3…Un is a number, then the nth term of
the sequence can be formulated
Un= a+(n-1)b
Un= nth term
a=U1= first term
b= difference/ difference
first question example
-3,2,7……
a= -3
b= 2-(-3) = 5
U20= -3+( 20-1) 5
= -3 +19.5
= -3+ 95
= 93
second question example
If an arithmetic sequence has the 7th and 13th
terms 31 and 55 respectively, the 33rd term of the
sequence is?
U7= a+6b
31= a+6b
U13= a+12b
55= a+12b
31= a+6b
31= a+ 6(4)
31= a+24
31-24=a
a= 7
31= a + 6b
55= a + 12b -24= -6b
b= -24/-6= 4
U33= 7+ (33-1) 4
= 7+32.4
= 7+128
= 135
The 33rd term of the sequence is 135
1
[Sn= 𝑛 (𝑎 + 𝑈𝑛) We use this formula if the last
2
term is known]
1
Sn= 𝑛 (2𝑎 + (𝑛 − 1)𝑏)
2
n= the sum of the first n terms
example
find the first 100 terms of the series
1+3+5+7+9…Un
answer
1
Sn= 𝑛(2𝑎 + (𝑛 − 1)𝑏)
Sn=
2
1
2
.100 (2.1 + (100 − 1)2)
S100= 50 (2+99.2)
S100= 50 (2+198)
S100= 50 x 200 = 10000
…