The first term of a sequence is the initial value or element from which the sequence begins. It is typically denoted as ( a_1 ) or ( a(1) ), depending on the notation used. This term sets the foundation for the subsequent terms that follow according to the sequence's defined rule or pattern.
That depends what the pattern of the sequence is.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
no
3
If the first two numbers are 0, 1 or -1 (not both zero) then you get an alternating Fibonacci sequence.
That depends what the pattern of the sequence is.
a + 99d where 'a' is the first term of the sequence and 'd' is the common difference.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4
no
3
4,8,12,16,20
If the first two numbers are 0, 1 or -1 (not both zero) then you get an alternating Fibonacci sequence.
To find the 6th term of a geometric sequence, you need the first term and the common ratio. The formula for the nth term in a geometric sequence is given by ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number. Please provide the first term and common ratio so I can calculate the 6th term for you.
The given sequence is an arithmetic sequence with a common difference of 4 between each term. To find the nth term of an arithmetic sequence, we use the formula: nth term = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number. In this case, the first term (a) is -3, the common difference (d) is 4, and the term number (n) is the position in the sequence. So, the nth term of the given sequence is -3 + (n-1)4 = 4n - 7.
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 first four terms are 3 9 27 81 and 729 is the 6th term.