Explain all steps and strategy not answers
- If d = 3 and n= 30 and S30 = 1875, find a and S5.
- Write the first 7 terms if a = 4 and d = 2.
- Write the first 7 terms if a = 6 and d = -1/2.
- If the 2nd term = -2 and the 5th = 43, write the first 7 terms.
- If the 3rd term = 5/2 and the 5th = -3/2, write the first 7 terms.
- A beach now has an area of 9500m2 but is eroding such that it loses 100m2 more of its area each year than during the previous year. If it lost 400m2 during the last year, what will be its area 8 years from now?
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ReplyDeletequestion 2
ReplyDeletea = 4
d = 2
staring with 4 keep adding 2 to the previous term until you reach the seventh term
4, 6, 8, 10, 12, 14, 16
question 3
ReplyDeletea = 6
d = -1/2
since we are starting at (a) and adding(-1/2)
we can say that we are minusing 1/2 from the previous term, so
6, 5.5, 5, 4.5, 4, 3.5, 3
question 4
ReplyDeletesolving
a +d = -2.....eq 1
a + 4d = 43.....eq 2
by elimination
equation 2 - 1
3d = 45
d = 45/3
d = 15
sub. d = 15 in equation 2
a + 4d = 43
a = 43 - 60
a = -17
since we found the unknowns
we can then put them in our formula
a + (n-1)d
ans.
-17, -2, 13, 28, 43, 58, 73
If the 3rd term = 5/2 and the 5th = -3/2, write the first 7 terms.
ReplyDeletea +2d = 5/2.....eq 1
a + 4d = -3/2.....eq 2
by elimination
equation 1 - 2
-2d = 4
d = 4/-2
d = -2
sub. d = -2 in equation 2
a + 2d = 5/2
a = 5/2 + 4
a = 13/2
since we found the unknowns
we can then put them in our formula
a + (n-1)d
ans.
13/2, 9/2, 5/2, 1/2, -3/2, -7/2, -11/2
question 6
ReplyDeleted = 100m2
a = 400m2
using the formula Sn = n/2[2a+(n-1)d]
we can find the 8th term by replacing 8 for n
so S8 = 8/2[2*400(8 - 1)100
= 6000m2 will errode in 8 years
new area = 9500 -6000
= 3500m2
question 1
ReplyDeleted = 3
n = 30
S30 = 1875
S30 = a + (30-1)3
1875 = a + 87
a = 1875 - 87
a = 1788
S5 = 1788(5-1)3
= 1800
someone, please check over my and correct any of my mistakes
ReplyDeletehmmm.....
ReplyDeleteshotta for question 4 there is an error..
ReplyDelete{
solving
a +d = -2.....eq 1
a + 4d = 43.....eq 2
by elimination
equation 2 - 1
3d = 45
equation 2 - 1
3d = 45
d = 45/3
d = 15
}
you didnt subtract the 2 from 43 ..
number 2
ReplyDeletea = 4
d = 2
starting with the first term which is 4, by adding 2 till you reach the 7th term you get
=4, 6, 8, 10, 12, 14, 16
number 6
ReplyDeleted = 100m2
a = 400m2
formula Sn = n/2 [2a + (n-1) d]
n=8
so S8 = 8/2 [2*400 (8 - 1)100
= 6000m2 will erode in 8 years
after eight years the beach would be= 9500 -6000
= 3500m2
d = 3 and n= 30 and S30 = 1875
ReplyDelete1875 = a + (30-1) 3
1875 = a + 29 *3
1875 -87 = a
a =1788
So S5 = 1788 + (5-1) 3
= 5376
I am not to clear on my approach for the second part can someone help me please
ReplyDeletefisrt 7 terms if a = 4 and d = 2.
ReplyDeletea + (n-1) d
SO because the common difference is 2 then all you need to do is add 2 to the fist term until you have seven terms