The formula is
Un = n*(-1)n+1
-1,-2,-3 10-1=9 9-2=7 7-3=4
the formula is: Sn= n [2(A1)+(n - 1)d] 2 for example the given sequence is when A1 = 4 and n = 10 when d = 2 here is the solution: Sn = 4 [2(4)+(10 - 1)2] 2 Sn= 2 [6+(9)(2) Sn = 2 [6+18] Sn = 2 (24) Sn = 48 see?
Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
456789
50
10-2x for x = 0, 1, 2, 3, ... Since the domain of an arithmetic sequence is the set of natural numbers, then the formula for the nth term of the given sequence with the first term 10 and the common difference -2 is an = a1 + (n -1)(-2) = 10 - 2n + 2 = 12 - 2n.
-1,-2,-3 10-1=9 9-2=7 7-3=4
10
the formula is: Sn= n [2(A1)+(n - 1)d] 2 for example the given sequence is when A1 = 4 and n = 10 when d = 2 here is the solution: Sn = 4 [2(4)+(10 - 1)2] 2 Sn= 2 [6+(9)(2) Sn = 2 [6+18] Sn = 2 (24) Sn = 48 see?
10 - 4n
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!
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
What is the formula for the number sequence 3 7 12 18 25...? This series is similar to the triangular number sequence 1 3 6 10 15 21.... with the formula n(n+1)/2. So for the number sequence 3 7 12 18 25... I derived a new formula by adding 2n to n(n+1)/2 to get this simplified formula: [(n*n) + 5n)]/2 (or n squared plus 5n all divided by two) when n=1, we get [(1*1) + 5(1)]/2=(1+5)/2= 6/2=3 when n=2, we get [(2*2) + 5(2)]/2=(4+10)/2=14/2=7 when n=3, we get [(3*3) + 5(3)]/2=(9+15)/2=24/2=12 when n=4, we get [(4*4) + 5(4)]/2=(16+20)/2=36/2=18 when n=5, we get [(5*5) + 5(5)]/2=(25+25)/2=50/2=25 If we want to know the 10th number in this series, we substitute n by 10 in our formula, we get [(10*10) + 5(10)]/2=(100+50)/2=150/2 = 75
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
The answer depends on what the explicit rule is!
Assuming each term is 3 MORE than the previous term t(n) = -13 + 3*n where n = 1, 2, 3, ...
The explicit formula for a sequence is a formula that allows you to find the nth term of the sequence directly without having to find all the preceding terms. To find the explicit formula for a sequence, you need to identify the pattern or rule that governs the sequence. This can involve looking at the differences between consecutive terms, the ratios of consecutive terms, or any other mathematical relationship that exists within the sequence. Once you have identified the pattern, you can use it to create a formula that will generate any term in the sequence based on its position (n) in the sequence.