To find the 53rd term of an arithmetic sequence, you can use the formula for the nth term: ( a_n = a_1 + (n-1) \cdot d ). Here, ( a_1 = 784 ), ( d = -6 ), and ( n = 53 ). Plugging in the values, we get ( a_{53} = 784 + (53-1) \cdot (-6) = 784 + 52 \cdot (-6) = 784 - 312 = 472 ). Therefore, the 53rd term is 472.
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.
To find the first three terms of an arithmetic sequence with a common difference of -5, we first need the last term. If we denote the last term as ( L ), the terms can be expressed as ( L + 10 ), ( L + 5 ), and ( L ) for the first three terms, since each term is derived by adding the common difference (-5) to the previous term. Thus, the first three terms would be ( L + 10 ), ( L + 5 ), and ( L ).
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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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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To find the first three terms of an arithmetic sequence with a common difference of -5, we first need the last term. If we denote the last term as ( L ), the terms can be expressed as ( L + 10 ), ( L + 5 ), and ( L ) for the first three terms, since each term is derived by adding the common difference (-5) to the previous term. Thus, the first three terms would be ( L + 10 ), ( L + 5 ), and ( L ).
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 ).
In an arithmetic sequence, "a" typically represents the first term of the sequence. An arithmetic sequence is defined by a constant difference between consecutive terms, known as the common difference (d). The n-th term of the sequence can be expressed as ( a_n = a + (n-1)d ), where ( a_n ) is the n-th term, ( a ) is the first term, and ( n ) is the term number.