Answer:
The first term of the geometric series is 1
Step-by-step explanation:
In this question, we are tasked with calculating the first term of a geometric series, given the common ratio, and the sum of the first 8 terms.
Mathematically, the sum of terms in a geometric series can be calculated as;
S = a(r^n-1)/( r-1)
where a is the first term that we are looking for
r is the common ratio which is 3 according to the question
n is the number of terms which is 8
S is the sum of the number of terms which is 3280 according to the question
Plugging these values, we have
3280 = a(3^8 -1)/(3-1)
3280 = a( 6561-1)/2
3280 = a(6560)/2
3280 = 3280a
a = 3280/3280
a = 1
Answer:
7
Step-by-step explanation:
21/3
3 will council it self one and 21 7times
Answer:
(3x+4)(5x+7)
Step-by-step explanation:
15x^2
+41x+28
Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2
+ax+bx+28. To find a and b, set up a system to be solved.
a+b=41
ab=15×28=420
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.
1,420
2,210
3,140
4,105
5,84
6,70
7,60
10,42
12,35
14,30
15,28
20,21
Calculate the sum for each pair.
1+420=421
2+210=212
3+140=143
4+105=109
5+84=89
6+70=76
7+60=67
10+42=52
12+35=47
14+30=44
15+28=43
20+21=41
The solution is the pair that gives sum 41.
a=20
b=21
Rewrite 15x^2
+41x+28 as (15x^2
+20x)+(21x+28).
(15x^2
+20x)+(21x+28)
Factor out 5x in the first and 7 in the second group.
5x(3x+4)+7(3x+4)
Factor out common term 3x+4 by using distributive property.
(3x+4)(5x+7)
Answer:
$32.30 each week
Step-by-step explanation:
Deposit = 15% = $34.20
⇒ total cost of camp = (34.20 ÷ 15) x 100 = $228
Balance left after deposit = 228 - 34.20 = $193.80
If paying the remaining balance in 6 weekly installments,
⇒ weekly payment = 193.80 ÷ 6 = $32.30
