QuestionFind the 3rd term of the sequence defined by: $a_1 = -6$ , $a_n = a_{n-1} + 2$ . A. -10 B. -2 C. -18 D. -4

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, $a1$ , is -6. . The recursive formula for the sequence is $a_n = a_{n-1} +$ , which means each term is more than the previous term.

STEP 2

We can find the second term of the sequence by substituting $n=2$ into the recursive formula.
$a2 = a_{2-1} +2$

STEP 3

Substitute $a1$ into the equation to find $a2$ .
$a2 = a1 +2 = -6 +2$

STEP 4

Calculate the value of $a2$ .
$a2 = -6 +2 = -4$

STEP 5

Now, we can find the third term of the sequence by substituting $n=3$ into the recursive formula.
$a3 = a_{3-1} +2$

STEP 6

Substitute $a2$ into the equation to find $a3$ .
$a3 = a2 +2 = -4 +2$

STEP 7

Calculate the value of $a3$ .
$a3 = -4 +2 = -2$ So, the third term in the sequence is -2. Therefore, the answer is B. -2.

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QuestionFind the 3rd term of the sequence defined by: $a_1 = -6$ , $a_n = a_{n-1} + 2$ . A. -10 B. -2 C. -18 D. -4

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, $a1$ , is -6. . The recursive formula for the sequence is $a_n = a_{n-1} +$ , which means each term is more than the previous term.

STEP 2

We can find the second term of the sequence by substituting $n=2$ into the recursive formula.
$a2 = a_{2-1} +2$

STEP 3

Substitute $a1$ into the equation to find $a2$ .
$a2 = a1 +2 = -6 +2$

STEP 4

Calculate the value of $a2$ .
$a2 = -6 +2 = -4$

STEP 5

Now, we can find the third term of the sequence by substituting $n=3$ into the recursive formula.
$a3 = a_{3-1} +2$

STEP 6

Substitute $a2$ into the equation to find $a3$ .
$a3 = a2 +2 = -4 +2$

STEP 7

Calculate the value of $a3$ .
$a3 = -4 +2 = -2$ So, the third term in the sequence is -2. Therefore, the answer is B. -2.

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QuestionFind the 3rd term of the sequence defined by: a1=−6a_1 = -6a1​=−6, an=an−1+2a_n = a_{n-1} + 2an​=an−1​+2. A. -10 B. -2 C. -18 D. -4

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, a1a1a1, is -6. . The recursive formula for the sequence is an=an−1+a_n = a_{n-1} +an​=an−1​+, which means each term is more than the previous term.

STEP 2

We can find the second term of the sequence by substituting n=2n=2n=2 into the recursive formula.a2=a2−1+2a2 = a_{2-1} +2a2=a2−1​+2

STEP 3

Substitute a1a1a1 into the equation to find a2a2a2.a2=a1+2=−6+2a2 = a1 +2 = -6 +2a2=a1+2=−6+2

STEP 4

Calculate the value of a2a2a2.a2=−6+2=−4a2 = -6 +2 = -4a2=−6+2=−4

STEP 5

Now, we can find the third term of the sequence by substituting n=3n=3n=3 into the recursive formula.a3=a3−1+2a3 = a_{3-1} +2a3=a3−1​+2

STEP 6

Substitute a2a2a2 into the equation to find a3a3a3.a3=a2+2=−4+2a3 = a2 +2 = -4 +2a3=a2+2=−4+2

STEP 7

Calculate the value of a3a3a3.a3=−4+2=−2a3 = -4 +2 = -2a3=−4+2=−2So, the third term in the sequence is -2. Therefore, the answer is B. -2.

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QuestionFind the 3rd term of the sequence defined by: $a_1 = -6$ , $a_n = a_{n-1} + 2$ . A. -10 B. -2 C. -18 D. -4

Assumptions1. The first term of the sequence, $a1$ , is -6. . The recursive formula for the sequence is $a_n = a_{n-1} +$ , which means each term is more than the previous term.

We can find the second term of the sequence by substituting $n=2$ into the recursive formula.
$a2 = a_{2-1} +2$

Substitute $a1$ into the equation to find $a2$ .
$a2 = a1 +2 = -6 +2$

Calculate the value of $a2$ .
$a2 = -6 +2 = -4$

Now, we can find the third term of the sequence by substituting $n=3$ into the recursive formula.
$a3 = a_{3-1} +2$

Substitute $a2$ into the equation to find $a3$ .
$a3 = a2 +2 = -4 +2$

Calculate the value of $a3$ .
$a3 = -4 +2 = -2$ So, the third term in the sequence is -2. Therefore, the answer is B. -2.