Series. Arithmetic. Help?
okay my online math class doesnt explain this. someone please help me. show me how to do examples like this. i need to know how to before i take my test. thank
Find the sum for the positive two-digit integers ending in 4.
A)576 B)324 C) 486 D) 325
Find the sum for the positive three-digit integers divisible by 6. A)920 
17650 C)82350 D) 140220
Determine the sum for the positive two-digit integers that are not divisible by 5.
A)3960 1640 C)2830 D)4550
Find S20 if the series 1+1.1+... is arithmetic.
A)2.9 B)1.9 C)39 D) 78
Comments
1)
first two digit number ending with 4 = 14
last two digit number ending with 4 = 94
so the series is
14,24,34.........94
a1 = 14, d = 10, n = 9
S(9) = n/2[a1+an] = 9/2[14+94] = 486
2)
first three digit number divisible by 6 = 102
the series is
102, 108, 114, ...............996
a1 = 102, d = 6
an = a1+(n-1)d
996 = 102 + (n-1)6
6(n-1) = 894
n-1 = 894/6 = 149
n = 150
s(150) = n/2[a1+an] = 150/2[102+996] = 82350
3)
The first two digit number = 10
The last two digit number = 99
total terms = 90
The total sum of all the two digits = 90/2[10+99] = 4905 ---eqn(1)
The first two digit number divisible by 5 = 10
the series is 10, 15,20,......... 95
a1 = 10, d= 5, n = 18
The sum of numbers divisible by 5 is 18/2[10+95] = 945----eqn(2)
so the sum of two digit numbers that are not divisible by 5 is
eqn(1) - eqn(2) = 4905 - 945 = 3960
4)
1, 1.1 ......
a1 = 1, d = 0.1 , n = 20
s20 = n/2[2a1+(n-1)d]
=20/2[2+19(0.1)] = 10(3.9) = 39