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[Bruno_]

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5,11,17,23

Type of sequence:
A23:
S23:
Sum of the series:

 

[🤖]

To determine the type of sequence, we need to find the difference between consecutive terms.

The difference between consecutive terms is:
11 - 5 = 6
17 - 11 = 6
23 - 17 = 6

Since the difference between consecutive terms is constant (6), we can conclude that the sequence is an arithmetic sequence.

To find the nth term of an arithmetic sequence, we can use the formula:
An = A1 + (n - 1)d

where An is the nth term, A1 is the first term, n is the position of the term, and d is the common difference.

For this sequence, the first term (A1) is 5 and the common difference (d) is 6.

To find the 23rd term (A23), we substitute the values into the formula:
A23 = 5 + (23 - 1) * 6 = 5 + 22 * 6 = 5 + 132 = 137

Therefore, the 23rd term of the sequence is 137 (A23 = 137).

To find the sum of the series, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(A1 + An)

where Sn is the sum of the series, n is the number of terms, A1 is the first term, and An is the last term.

For this sequence, the number of terms is 23, the first term (A1) is 5, and the last term (An) is 137.

Substituting the values into the formula:
Sn = (23/2)(5 + 137) = 11.5 * 142 = 1637

Therefore, the sum of the series is 1637 (Sn = 1637).

To summarize:
Type of sequence: Arithmetic sequence
A23: 137
S23: 1637
Sum of the series: 1637

 

[Bruno_]

Bot, show the complete solution

64, -32 ,16, -8, 4

Type of sequence:
A23:
S23:
Sum of the series:

To determine the type of sequence, we need to find the difference between consecutive terms.

The difference between consecutive terms is:
11 - 5 = 6
17 - 11 = 6
23 - 17 = 6

Since the difference between consecutive terms is constant (6), we can conclude that the sequence is an arithmetic sequence.

To find the nth term of an arithmetic sequence, we can use the formula:
An = A1 + (n - 1)d

where An is the nth term, A1 is the first term, n is the position of the term, and d is the common difference.

For this sequence, the first term (A1) is 5 and the common difference (d) is 6.

To find the 23rd term (A23), we substitute the values into the formula:
A23 = 5 + (23 - 1) * 6 = 5 + 22 * 6 = 5 + 132 = 137

Therefore, the 23rd term of the sequence is 137 (A23 = 137).

To find the sum of the series, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(A1 + An)

where Sn is the sum of the series, n is the number of terms, A1 is the first term, and An is the last term.

For this sequence, the number of terms is 23, the first term (A1) is 5, and the last term (An) is 137.

Substituting the values into the formula:
Sn = (23/2)(5 + 137) = 11.5 * 142 = 1637

Therefore, the sum of the series is 1637 (Sn = 1637).

To summarize:
Type of sequence: Arithmetic sequence
A23: 137
S23: 1637
Sum of the series: 1637

Bot, show the complete solution

64, -32 ,16, -8, 4

Type of sequence:
A23:
S23:
Sum of the series: