H&J is the answer I just took the test
Answer:
108 th term is zero
Step-by-step explanation:
The nth term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₉ = 99 and a₉₉ = 9 then
a₁ + 8d = 99 → (1)
a₁ + 98d = 9 → (2)
Subtract (1) from (2) term by term to eliminate a₁
0 + 90d = - 90
90d = - 90 ( divide both sides by 90 )
d = - 1
Substitute d = - 1 into (1) for value of a₁
a₁ + 8(- 1) = 99
a₁ - 8 = 99 ( add 8 to both sides )
a₁ = 107
Then
107 - (n - 1) = 0
107 - n + 1 = 0
- n + 108 = 0 ( subtract 108 from both sides )
- n = - 108 ( multiply both sides by - 1 )
n = 108
The 108th term is zero
200×60 cause 1 min is 60 sec
then divde 3
(i) The simultaneous equations in a, b and c are a+b+c = 7 , 4a+2b+c = 9 & 9a+3b+c = 13
(ii) Expression for nth term = n²-n+7
The first three terms of the sequence are 7, 9, 13
nth term = an²+bn+c
If we put n = 1 then,
1st term = a(1)²+b+c
⇒ a+b+c = 7 ......(1)
If we put n = 2 then,
2nd term = a(2)²+b×2+c
⇒ 4a+2b+c = 9 ........(2)
3rd term = a(3)²+b×3+c
⇒ 9a+3b+c = 13 .......(3)
Multiplying 4 with (1) and subtract (2) from (1) we get,
(4a+4b+4c)-(4a+2b+c)=28-9
⇒ 4a+4b+4c-4a-2b-c=19
⇒ 2b+3c=19 .....(4)
Multiplying 9 with (1) and subtract (3) from (1) we get,
(9a+9b+9c)-(9a+3b+c)=63-13
⇒ 9a+9b+9c-9a-3b-c=50
⇒ 6b+8c=50
⇒ 3b+4c=25 .....(5)
Multiplying 3 with (4) and multiplying 2 with (5), then subtract (5) from (4),
3(2b+3c)-2(3b+4c)=57-50
⇒ 6b+9c-6b-8c=7
⇒ c = 7
From (5),
3b+28 = 25
⇒ 3b = -3
⇒ b = -1
From (1),
a+(-1)+7 = 7
⇒ a-1=0
⇒ a=1
So, nth term = n²-n+7
Learn more about sequence here :
brainly.com/question/6561461
#SPJ10
Easy question
x=10
mECH=40
mHCD=50
mGCF=40
mECG=140
mGCD=13
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