the third and fourth terms of an arithmetic sequence are -3 and 0.?
how do i found the 1000th term
9 Answers
- 8 months ago
Since you're dealing with an AP(arithmetric sequence), let the nth term be Tn
Generally, Tn=a+(n-1)d
Where a=first term; n=number of terms; d=common difference
From the first point, 3rd term=-3 and from the second point, 4th term=0
This means,
T3=a+(3-1)d=-3
a+2d=-3..................1
Also, T4=a+(4-1)d=0
a+3d=0
a=-3d.......................2
Substitute a as -3d into equation 1;
-3d+2d=-3
-d=-3
d=3
Also, from equation 2, a=-3(3)=-9
Hence, a=-9, d=3
Tn=-9+(n-1)3
Tn=-9+3n-3=3n-12
Tn=3n-12
Finally, when n=1000
T1000=3(1000)-12
=3000-12
=2988
Hence, 1000th term is 2988
- ?Lv 78 months ago
-9, -6, -3, 0, ...
-9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, ...
a_n = 3 (n - 4)
The 1000th term is 2988
- ?Lv 68 months ago
I think of the difference as a "step."
-3 to 0 means it increases in steps of 3
You have the 4th term, which is 0.
You want the 1000th term which is 996 steps away.
So just add 996 step to the 4th term.
0 + 3*996 = 2988 is the 1000th term
- sepiaLv 78 months ago
The third and fourth terms of an arithmetic sequence are -3 and 0.
-9, -6, -3, 0, ...
a_n = 3 (n - 4)
The 1000th term is 3(996) = 2988.
- What do you think of the answers? You can sign in to give your opinion on the answer.
- Wayne DeguManLv 78 months ago
Common difference is 3
Hence, 2nd term is -6 and 1st term is -9
nth term is -9 + 3(n - 1)
i.e. 3n - 12
so, 1000th term is 3(1000) - 12 => 2988
:)>
- la consoleLv 78 months ago
For an arithmetic sequence:
a₁
a₂ = a₁ + d ← where d is the common difference, i.e.: 5
a₃ = a₂ + d = a₁ + 2d = - 3
a₄ = a₃ + d = a₁ + 3d = 0
You can obtain a system with 2 equations:
(1) : a₁ + 2d = - 3
(2) : a₁ + 3d = 0
Then you calculate (1) - (2):
(a₁ + 2d) - (a₁ + 3d) = - 3 - 0
a₁ + 2d - a₁ - 3d = - 3
d = 3
Recall a₃ = a₁ + 2d = - 3
a₁ + 2d = - 3
a₁ = - 3 - 2d → we've just seen that: d = 3
a₁ = - 9
Recall:
a₁
a₂ = a₁ + d
a₃ = a₁ + 2d
a₄ = a₁ + 3d
…and you can generalize writing:
a(n) = a₁ + (n - 1).d → for the 1000th term, n = 1000
a₁₀₀₀ = - 9 + (1000 - 1).3
a₁₀₀₀ = - 9 + (999 * 3)
a₁₀₀₀ = 2988
- Pramod KumarLv 78 months ago
nth term of an Arithmetic Sequence is given by -
T(n) = First term (suppose-a) + ( n-1 ) (common difference ( say d )
Hence ---
T(3) = a + ( 3 - 1 ) d = - 3
=> a + 2 d = - 3 .................... (1) Similarly --
T(4) = a + ( 4 - 1 ) d = 0
=> a + 3 d = 0 ............. (2)
from (1) and (2) we get
a = - 9 and d = 3
Hence T(1000) = - 9 + ( 1000 - 1 ) 3 = 3000 - 12 = 2988.......Answer
- Anonymous8 months ago
Difference is 3.
2nd tem is -6
1st term is -9
n-t term is a + (n-1)d
1000th term = -9 + (1000-1)3 = 2988
- 8 months ago
if -3 and 0 are third or fourth terms,it mean it is increasing by 3, so if we start from 0 we have 996 terms left to get to 1000 terms.
so the 1000th term is the term x how much it is increasing
we have 996 terms if we start from 0
996 x 3
=2988