In an arithmetic sequence, the nth term can be expressed as ( a_n = a + (n-1)d ), where ( a ) is the first term and ( d ) is the common difference. Given that the common difference ( d ) is 36 and the 20th term ( a_{20} = a + 19d ), we can set up the equation ( a + 19(36) = a + 684 ). To find the first term, we need additional information about the value of the 20th term; without that, we cannot determine the exact value of the first term ( a ).
What is the 14th term in the arithmetic sequence in which the first is 100 and the common difference is -4? a14= a + 13d = 100 + 13(-4) = 48
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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, the sequence 2, 5, 8, 11, 14 has a common difference of 3. Another example is 10, 7, 4, 1, which has a common difference of -3. In general, an arithmetic sequence can be expressed as (a_n = a_1 + (n-1)d), where (a_1) is the first term and (d) is the common difference.
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What is the 14th term in the arithmetic sequence in which the first is 100 and the common difference is -4? a14= a + 13d = 100 + 13(-4) = 48
It is a + 8d where a is the first term and d is the common difference.
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Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
The answer is two arithmetic sequences, both with a common difference of 3, alternating with one another, where the second series is greater than the first by the value of 2*A(0), ie twice the starting value.
From any term after the first, subtract the preceding term.
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For an Arithmetic Progression, Sum = 15[a + 7d].{a = first term and d = common difference} For a Geometric Progression, Sum = a[1-r^15]/(r-1).{r = common ratio }.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, the sequence 2, 5, 8, 11, 14 has a common difference of 3. Another example is 10, 7, 4, 1, which has a common difference of -3. In general, an arithmetic sequence can be expressed as (a_n = a_1 + (n-1)d), where (a_1) is the first term and (d) is the common difference.
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