Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
Since the difference between each term is '4' , then the first part of the formula is '4n'.
The formula is Un = n*(-1)n+1
The formula would be the previous number plus the next number minus 1.
a(n) = a(1) x r^n-1 In this case a(1) is 2 and r is 3 That makes the formula a(n) = 2 x 3^n-1
Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
The simplest formula isUn = (-8611*n^2 + 34477*n - 25082)/2 for n = 1, 2, 3.
Each term is 3 times greater than the previous term and so the next term will be 486
a recursive formula is always based on a preceding value and uses A n-1 and the formula must have a start point (an A1) also known as a seed value. unlike recursion, explicit forms can stand alone and you can put any value into the "n" and one answer does not depend on the answer before it. we assume the "n" starts with 1 then 2 then 3 and so on arithmetic sequence: an = a1 + d(n-1) this does not depend on a previous value
1135 millimeters is equal to 44.69 inches or 3.72 feet.
Finding the nth term is much simpler than it seems. For example, say you had the sequence: 1,4,7,10,13,16 Sequence 1 First we find the difference between the numbers. 1 (3) 4 (3) 7 (3) 10 (3) 13 (3) 16 The difference is the same: 3. So the start of are formula will be 3n. If it was 3n, the sequence would be 3,6,9,12,15,18 Sequence 2 But this is not our sequence. Notice that each number on sequence 2 is 2 more than sequence 1. this means are final formula will be: 3n+1 Test it out, it works!
Since the difference between each term is '4' , then the first part of the formula is '4n'.
The nth term of a sequence is the general formula for a sequence. The nth term of this particular sequence would be n+3. This is because each step in the sequence is plus 3 higher than the previous step.
There are different answers depending upon whether the sequence is an arithmetic progression, a geometric progression, or some other sequence. For example, the sequence 4/1 - 4/3 + 4/5 - 4/7 adds to pi
The formula is Un = n*(-1)n+1
There is no formula, but I can point out that: between the numbers you get: +1,+2,+3,+4+5... so the next term would be +6 or 21
There are infinitely many polynomials of order 4 that will give these as the first four numbers and any one of these could be "the" explicit formula. There are also non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. For example, t(n) = (-17*n^4 + 170*n^3 - 575*n^2 + 830*n - 400)/4 for n = 1, 2, 3, ... The Simplest, though is t(n) = 5*n^2 - 5*n + 2 for n = 1, 2, 3, ...