QuestionFind the 3rd term of the geometric sequence defined by $a_1=5$ and $a_n=a_{n-1} \cdot 3$ . A. 45 B. 11 C. 125 D. 15

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, $a1$ , is5. . The recursive formula for the sequence is $a_n = a_{n-1} \cdot3$ .

STEP 2

The recursive formula tells us that each term in the sequence is three times the previous term. So, to find the second term, we multiply the first term by.
$a2 = a1 \cdot$

STEP 3

Substitute the given value for $a1$ into the equation to calculate $a2$ .
$a2 =5 \cdot3$

STEP 4

Calculate the value of $a2$ .
$a2 = \cdot3 =15$

STEP 5

Now, to find the third term, we multiply the second term by3.
$a3 = a2 \cdot3$

STEP 6

Substitute the calculated value for $a2$ into the equation to calculate $a3$ .
$a3 =15 \cdot3$

STEP 7

Calculate the value of $a3$ .
$a3 =15 \cdot3 =45$ The third term of the sequence is45.

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QuestionFind the 3rd term of the geometric sequence defined by $a_1=5$ and $a_n=a_{n-1} \cdot 3$ . A. 45 B. 11 C. 125 D. 15

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, $a1$ , is5. . The recursive formula for the sequence is $a_n = a_{n-1} \cdot3$ .

STEP 2

The recursive formula tells us that each term in the sequence is three times the previous term. So, to find the second term, we multiply the first term by.
$a2 = a1 \cdot$

STEP 3

Substitute the given value for $a1$ into the equation to calculate $a2$ .
$a2 =5 \cdot3$

STEP 4

Calculate the value of $a2$ .
$a2 = \cdot3 =15$

STEP 5

Now, to find the third term, we multiply the second term by3.
$a3 = a2 \cdot3$

STEP 6

Substitute the calculated value for $a2$ into the equation to calculate $a3$ .
$a3 =15 \cdot3$

STEP 7

Calculate the value of $a3$ .
$a3 =15 \cdot3 =45$ The third term of the sequence is45.

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QuestionFind the 3rd term of the geometric sequence defined by a1=5a_1=5a1​=5 and an=an−1⋅3a_n=a_{n-1} \cdot 3an​=an−1​⋅3. A. 45 B. 11 C. 125 D. 15

Studdy Solution

STEP 1

Assumptions1. The first term of the sequence, a1a1a1, is5. . The recursive formula for the sequence is an=an−1⋅3a_n = a_{n-1} \cdot3an​=an−1​⋅3.

STEP 2

The recursive formula tells us that each term in the sequence is three times the previous term. So, to find the second term, we multiply the first term by.a2=a1⋅a2 = a1 \cdota2=a1⋅

STEP 3

Substitute the given value for a1a1a1 into the equation to calculate a2a2a2.a2=5⋅3a2 =5 \cdot3a2=5⋅3

STEP 4

Calculate the value of a2a2a2.a2=⋅3=15a2 = \cdot3 =15a2=⋅3=15

STEP 5

Now, to find the third term, we multiply the second term by3.a3=a2⋅3a3 = a2 \cdot3a3=a2⋅3

STEP 6

Substitute the calculated value for a2a2a2 into the equation to calculate a3a3a3.a3=15⋅3a3 =15 \cdot3a3=15⋅3

STEP 7

Calculate the value of a3a3a3.a3=15⋅3=45a3 =15 \cdot3 =45a3=15⋅3=45The third term of the sequence is45.

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QuestionFind the 3rd term of the geometric sequence defined by $a_1=5$ and $a_n=a_{n-1} \cdot 3$ . A. 45 B. 11 C. 125 D. 15

Assumptions1. The first term of the sequence, $a1$ , is5. . The recursive formula for the sequence is $a_n = a_{n-1} \cdot3$ .

The recursive formula tells us that each term in the sequence is three times the previous term. So, to find the second term, we multiply the first term by.
$a2 = a1 \cdot$

Substitute the given value for $a1$ into the equation to calculate $a2$ .
$a2 =5 \cdot3$

Calculate the value of $a2$ .
$a2 = \cdot3 =15$

Now, to find the third term, we multiply the second term by3.
$a3 = a2 \cdot3$

Substitute the calculated value for $a2$ into the equation to calculate $a3$ .
$a3 =15 \cdot3$

Calculate the value of $a3$ .
$a3 =15 \cdot3 =45$ The third term of the sequence is45.