The formula is
Un = n*(-1)n+1
-1,-2,-3 10-1=9 9-2=7 7-3=4
The sequence 4, 6, 8, 10 is an arithmetic sequence where each term increases by 2. The nth term formula can be expressed as ( a_n = 4 + (n - 1) \cdot 2 ). Simplifying this gives ( a_n = 2n + 2 ). Thus, the nth term of the sequence is ( 2n + 2 ).
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?
The sequence defined by the formula ( n^2 + 3n ) can be calculated by substituting the first three positive integers for ( n ). For ( n = 1 ), the term is ( 1^2 + 3(1) = 4 ); for ( n = 2 ), it is ( 2^2 + 3(2) = 10 ); and for ( n = 3 ), it is ( 3^2 + 3(3) = 18 ). Therefore, the first three terms of the sequence are 4, 10, and 18.
The sequence provided is an arithmetic sequence where the first term is 3 and the common difference is 2. The formula for the nth term of an arithmetic sequence is given by ( a_n = a_1 + (n-1)d ), where ( a_1 ) is the first term and ( d ) is the common difference. For the 10th term, ( a_{10} = 3 + (10-1) \times 2 = 3 + 18 = 21 ). Thus, the 10th term of the sequence is 21.
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 sequence 4, 6, 8, 10 is an arithmetic sequence where each term increases by 2. The nth term formula can be expressed as ( a_n = 4 + (n - 1) \cdot 2 ). Simplifying this gives ( a_n = 2n + 2 ). Thus, the nth term of the sequence is ( 2n + 2 ).
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!
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
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
The sequence defined by the formula ( n^2 + 3n ) can be calculated by substituting the first three positive integers for ( n ). For ( n = 1 ), the term is ( 1^2 + 3(1) = 4 ); for ( n = 2 ), it is ( 2^2 + 3(2) = 10 ); and for ( n = 3 ), it is ( 3^2 + 3(3) = 18 ). Therefore, the first three terms of the sequence are 4, 10, and 18.
The sequence provided is an arithmetic sequence where the first term is 3 and the common difference is 2. The formula for the nth term of an arithmetic sequence is given by ( a_n = a_1 + (n-1)d ), where ( a_1 ) is the first term and ( d ) is the common difference. For the 10th term, ( a_{10} = 3 + (10-1) \times 2 = 3 + 18 = 21 ). Thus, the 10th term of the sequence is 21.
The sequence consists of triangular numbers, which can be calculated using the formula ( T_n = \frac{n(n + 1)}{2} ). The numbers in the sequence correspond to ( T_1, T_3, T_5, T_6, T_7, T_8, T_9 ) respectively. Following this pattern, the next number is ( T_{10} = \frac{10(10 + 1)}{2} = 55 ). Therefore, the next number in the sequence is 72.