Question
1) Find the sum of the first 13 terms of the sequence: −3, −1, 1, 3, …
2) Find the sum of the first 15 terms of the arithmetic sequence: 10, 15, 20, 25, … ?
3) Find the sum of the first 11 terms of the arithmetic sequence: −4, 3, 10, 17, … ?
4) Find the sum of the first 19 terms of the arithmetic sequence: 9, 14, 19, 24, … ?
5) Find the sum of the integers from 8 and 35.
6) Find the sum of all even integers from 10 to 70.
7) Find the sum of all odd integers from 1 to 50.
8) Find the sum of the integers from 20 to 130 and are divisible by 5.
9) If the sum of the first 8 terms of an arithmetic sequence is 172 and its common difference is 3, what is the first term?
10) If the sum of the first 9 terms of an arithmetic sequence is 216 and its first term is 4, what is the common difference?
with solution..
−3−1+1+3+5+7+9+11
+13+15+17+19+21 = 117
=10+(15-1)5
=10+(14)5
3-(-4) = 7
10-3 = 7
17-10=7
14-9= 5 19-14=5
An= 9+(19-1)5
An= 9+90
A19= 99
a1= 10
a31=70
n=31 (because from 10-70 we have 31 even numbers)
s31= 31/2 (10+70)
s31= 1240
l=a+(n-1)d
49=1+(n-1)2
2n-2=48
2n=50
n=50/2
n=25
Sn=n/2(a+l)
=25/2(1+49)
=25/2(50)
=25(25)
formulas:
last term = first term + (n-1)d
Sn = n/2 (first term + last term)
given:
d= 5. last term= 130. first term= 20. n=?
solution:
last term = first term + (n-1)d
130 = 20 + (n-1)5
130-20 = (n-1)5
110 = (n-1)5
110 = (n-1) 5
----- ----------
5 5
22 = n-1
22+1 =n
23 = n
Sn = 23/2 (20+130)
Sn = 23/2 (150)
make it easier by dividing 150 to 2 first then multiply it to 23
Sn = 23 (75)
S8 = 8/2 [2(A1) + (8 - 1)3]
172 = 8/2 [2A1 + (7)3]
172 = 8/2 (2A1 + 21)
344 = 8 (2A1 + 21)
344 = 16A1 + 168
344 - 168 = 16A1
4+5=9
9+5=14
14+5=19
19+5=24
24+5=29
29+5=34
34+5=39
39+5=44
4+9+14+19+24+29+34+38+44=
