First verify the base case by inserting values so you can assume it holds for it n
for n+1 add the next term 6*(n+1) of the sum to both sides:
6 + 12 + 18 + ... + 6n +6(n+1)= 3n(n+1)+6(n+1)
=(n+1)(3n+6)
=3(n+1)(n+2)
=3(n+1)((n+1)+1)
=term if you had inserted n+1 instead of n, proving correctness
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Hello!
Each minute on a clock or watch is 6°, as you divide 360° by 60 minutes. As you can see, 32 minutes elapsed during the class. Therefore we just multiply.
32(6)=192
Therefore, our answer is B) 192.
I hope this helps!
To evaluate the series we proceed as follows:
2. -5,-15,-25,-35,-45
The common difference is (-15--5)=-10
thus the series is an arithmetic sequence hence the explicit formula will be:
an=a+(n-1)d
thus the formula for the series is:
an=-5+(n-1)(-10)
an=-10n+5
4. 0.5, 0.25,0,...,-0.75
The common difference =0.25-0.5=-0.25
The sequence is an arithmetic sequence:
the explicit formula will be:
an=0.5-0.25(n-1)
an=-0.25n+0.75
thus
n=4
a4=-0.25*4+0.75=-0.25
when n=5
a5=-0.25*5+0.75=-0.5
when n=6
a6=-0.25*6+0.75=-0.75
the missing values are -0.25 and -0.5
6] 4.5,5.6,6.7, ....,11.1
common difference=5.6-4.5=1.1
the sequence is an arithmetic sequence
The explicit formula is:
an=4.5+1.1(n-1)
an=1.1n+3.4
when n=4
an=1.1*4+3.4
a4=7.8
when n=5
a5=1.1*5+3.4
a5=8.9
a6=1.1*6+3.4
a6=10
the missing values are: 7.8, 8.9, 10
Answer:
B
Step-by-step explanation:
fourth term
A(4)= 7 - ( 4-1)(-3)
=-2
seventh term
A(7)= 7 - (7-1)(-3)
=-11
tenth term
A(10) = 7 - (10-1)(-3)
= -20
Decrease percentage = (120-52)/120 ×100 = 68/120 =56.66..%
On rounding off,
Percentage = 57%
HOPE THIS WILL HELP YOU
