Arithmetic and Geometric Series and Their Sums!

Hello everyone,

I hope everyone had a wonderful weekend!

To find the sum of the ___ terms of an arithmetic series

Sn=n(t1+tn)/2

To find the sum of the ___ terms of a geometric series

Sn=t1(1-r^n)/1-r

Series- a list of numbers that are added together.

2+4+6+8+...

Example 1:

For the arithmetic series, find the specified sum.

S10: t1=3, t10=39

S10= 10(3+39)/2

S10=210

Example 2:

For the arithmetic series, find the specified sum.

S50=: 5+10+15+...

S50=50(5+250)/2

S50=6375

tn=t1(n-1)d

tn=5+(50-1)5

tn=5+250-5

tn=250

Example 3:

Find the sum of all multiples of 3 between 1 and 1000.

3+6+...999

S333=333(3+999)/2

S=166833

999=3+(n-1)-3

999=3n

n=333

Example 4:

Find the sum of all positive 3-digit numbers whose last digit is 3.

103+113+...993

S90=90(103+993)/2

S90=49320

tn=t1+(n-1)d

993=103+(n-1)10

993=103+10n-10

993=93+10n

900=10n

n=90

Example 5:

Find the sum of all positive 3-digit numbers divisible by 6.

102+108+...996

S150=150(102+996)/2

S150=82350

996=102+(n-1)6

996=102+6n-6

996=96+6n

900=6n

n=150

Example 6:

Find the sum of the series 1-3+5-7+9-11+...+1001.

S501=501(1+1001)/2

S501=251001

1001=1+(n-1)2

1001=1+2n-2

1001=-1+2n

1002=2n

n=501