Math / Algebra

QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+4$ Work out the $5^{\text {th }}$ term of this sequence.

Studdy Solution

STEP 1

1. We are given the sequence defined by the term rule $T(n) = n^2 + 4$ .
2. We need to find the 5th term of this sequence.

STEP 2

1. Identify the term rule for the sequence.
2. Substitute $n = 5$ into the term rule.
3. Calculate the value of the 5th term.

STEP 3

Identify the term rule for the sequence:
The term rule is given as $T(n) = n^2 + 4$ .

STEP 4

Substitute $n = 5$ into the term rule:
$T(5) = 5^2 + 4$

STEP 5

Calculate $5^2$ :
$5^2 = 25$

STEP 6

Substitute the value of $5^2$ into the expression for $T(5)$ and calculate:
$T(5) = 25 + 4$ $T(5) = 29$
The 5th term of the sequence is:
$\boxed{29}$

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QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+4$ Work out the $5^{\text {th }}$ term of this sequence.

Studdy Solution

STEP 1

1. We are given the sequence defined by the term rule $T(n) = n^2 + 4$ .
2. We need to find the 5th term of this sequence.

STEP 2

1. Identify the term rule for the sequence.
2. Substitute $n = 5$ into the term rule.
3. Calculate the value of the 5th term.

STEP 3

Identify the term rule for the sequence:
The term rule is given as $T(n) = n^2 + 4$ .

STEP 4

Substitute $n = 5$ into the term rule:
$T(5) = 5^2 + 4$

STEP 5

Calculate $5^2$ :
$5^2 = 25$

STEP 6

Substitute the value of $5^2$ into the expression for $T(5)$ and calculate:
$T(5) = 25 + 4$ $T(5) = 29$
The 5th term of the sequence is:
$\boxed{29}$

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QuestionThe nth n^{\text {th }}nth term rule for a sequence is T(n)=n2+4T(n)=n^{2}+4T(n)=n2+4 Work out the 5th 5^{\text {th }}5th term of this sequence.

Studdy Solution

STEP 1

1. We are given the sequence defined by the term rule T(n)=n2+4 T(n) = n^2 + 4 T(n)=n2+4.2. We need to find the 5th term of this sequence.

STEP 2

1. Identify the term rule for the sequence.2. Substitute n=5 n = 5 n=5 into the term rule.3. Calculate the value of the 5th term.

STEP 3

Identify the term rule for the sequence:The term rule is given as T(n)=n2+4 T(n) = n^2 + 4 T(n)=n2+4.

STEP 4

Substitute n=5 n = 5 n=5 into the term rule:T(5)=52+4 T(5) = 5^2 + 4 T(5)=52+4

STEP 5

Calculate 52 5^2 52:52=25 5^2 = 25 52=25

STEP 6

Substitute the value of 52 5^2 52 into the expression for T(5) T(5) T(5) and calculate:T(5)=25+4 T(5) = 25 + 4 T(5)=25+4 T(5)=29 T(5) = 29 T(5)=29 The 5th term of the sequence is:29 \boxed{29} 29​

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QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+4$ Work out the $5^{\text {th }}$ term of this sequence.

1. We are given the sequence defined by the term rule $T(n) = n^2 + 4$ .
2. We need to find the 5th term of this sequence.

1. Identify the term rule for the sequence.
2. Substitute $n = 5$ into the term rule.
3. Calculate the value of the 5th term.

Identify the term rule for the sequence:
The term rule is given as $T(n) = n^2 + 4$ .

Substitute $n = 5$ into the term rule:
$T(5) = 5^2 + 4$

Calculate $5^2$ :
$5^2 = 25$

Substitute the value of $5^2$ into the expression for $T(5)$ and calculate:
$T(5) = 25 + 4$ $T(5) = 29$
The 5th term of the sequence is:
$\boxed{29}$