Question1) Find the expression for the sequence: -66, -132, -198, -264 with $n=1$ for the first term. $a_n=$
2) Find the expression for the sequence: 7, 14, 21, 28 with $n=1$ for the first term. $a_n=$

Studdy Solution

STEP 1

Assumptions1. The sequences are arithmetic sequences, which means the difference between consecutive terms is constant. . The variable $n$ represents the position of a term in the sequence, where $n=1$ for the first term.

STEP 2

For the first sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 = -132 - (-66)$

STEP 3

Calculate the common difference for the first sequence.
$d = -132 - (-66) = -66$

STEP 4

The general form of an arithmetic sequence is $a_n = a1 + (n-1) \cdot d$ . For the first sequence, $a1 = -66$ and $d = -66$ . Substituting these values into the general form gives us the expression for the first sequence.
$a_n = -66 + (n-1) \cdot -66$

STEP 5

implify the expression for the first sequence.
$a_n = -66n +66$

STEP 6

For the second sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 =14 -$

STEP 7

Calculate the common difference for the second sequence.
$d =14 -7 =7$

STEP 8

The general form of an arithmetic sequence is $a_n = a1 + (n-1) \cdot d$ . For the second sequence, $a1 =7$ and $d =7$ . Substituting these values into the general form gives us the expression for the second sequence.
$a_n =7 + (n-1) \cdot7$

STEP 9

implify the expression for the second sequence.
$a_n =7n$ The expressions for the sequences are) $a_n = -66n +66$ 2) $a_n =7n$

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Question1) Find the expression for the sequence: -66, -132, -198, -264 with $n=1$ for the first term. $a_n=$
2) Find the expression for the sequence: 7, 14, 21, 28 with $n=1$ for the first term. $a_n=$

Studdy Solution

STEP 1

Assumptions1. The sequences are arithmetic sequences, which means the difference between consecutive terms is constant. . The variable $n$ represents the position of a term in the sequence, where $n=1$ for the first term.

STEP 2

For the first sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 = -132 - (-66)$

STEP 3

Calculate the common difference for the first sequence.
$d = -132 - (-66) = -66$

STEP 4

The general form of an arithmetic sequence is $a_n = a1 + (n-1) \cdot d$ . For the first sequence, $a1 = -66$ and $d = -66$ . Substituting these values into the general form gives us the expression for the first sequence.
$a_n = -66 + (n-1) \cdot -66$

STEP 5

implify the expression for the first sequence.
$a_n = -66n +66$

STEP 6

For the second sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 =14 -$

STEP 7

Calculate the common difference for the second sequence.
$d =14 -7 =7$

STEP 8

The general form of an arithmetic sequence is $a_n = a1 + (n-1) \cdot d$ . For the second sequence, $a1 =7$ and $d =7$ . Substituting these values into the general form gives us the expression for the second sequence.
$a_n =7 + (n-1) \cdot7$

STEP 9

implify the expression for the second sequence.
$a_n =7n$ The expressions for the sequences are) $a_n = -66n +66$ 2) $a_n =7n$

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Question1) Find the expression for the sequence: -66, -132, -198, -264 with n=1n=1n=1 for the first term. an=a_n=an​=2) Find the expression for the sequence: 7, 14, 21, 28 with n=1n=1n=1 for the first term. an=a_n=an​=

Studdy Solution

STEP 1

Assumptions1. The sequences are arithmetic sequences, which means the difference between consecutive terms is constant. . The variable nnn represents the position of a term in the sequence, where n=1n=1n=1 for the first term.

STEP 2

For the first sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.d=a2−a1=−132−(−66)d = a2 - a1 = -132 - (-66)d=a2−a1=−132−(−66)

STEP 3

Calculate the common difference for the first sequence.d=−132−(−66)=−66d = -132 - (-66) = -66d=−132−(−66)=−66

STEP 4

STEP 5

implify the expression for the first sequence.an=−66n+66a_n = -66n +66an​=−66n+66

STEP 6

For the second sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.d=a2−a1=14−d = a2 - a1 =14 -d=a2−a1=14−

STEP 7

Calculate the common difference for the second sequence.d=14−7=7d =14 -7 =7d=14−7=7

STEP 8

STEP 9

implify the expression for the second sequence.an=7na_n =7nan​=7nThe expressions for the sequences are) an=−66n+66a_n = -66n +66an​=−66n+66 2) an=7na_n =7nan​=7n

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question1) Find the expression for the sequence: -66, -132, -198, -264 with $n=1$ for the first term. $a_n=$
2) Find the expression for the sequence: 7, 14, 21, 28 with $n=1$ for the first term. $a_n=$

Assumptions1. The sequences are arithmetic sequences, which means the difference between consecutive terms is constant. . The variable $n$ represents the position of a term in the sequence, where $n=1$ for the first term.

For the first sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 = -132 - (-66)$

Calculate the common difference for the first sequence.
$d = -132 - (-66) = -66$

implify the expression for the first sequence.
$a_n = -66n +66$

For the second sequence, we need to determine the common difference between the terms. This can be done by subtracting the second term from the first term.
$d = a2 - a1 =14 -$

Calculate the common difference for the second sequence.
$d =14 -7 =7$

implify the expression for the second sequence.
$a_n =7n$ The expressions for the sequences are) $a_n = -66n +66$ 2) $a_n =7n$