Math / Algebra

QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+3$
Work out the $5^{\text {th }}$ term of this sequence.

Studdy Solution

STEP 1

What is this asking? Given a formula that tells us the value of any term in a sequence, we need to find the value of the 5th term. Watch out! Make sure to substitute the correct value for $n$ and follow the order of operations (PEMDAS/BODMAS) carefully!

STEP 2

1. Substitute and Evaluate

STEP 3

Alright, let's dive in!
We've got this awesome formula $T(n) = n^2 + 3$ that tells us the value of the $n$ th term in a sequence.
We want to find the 5th term, so we're going to substitute $n = 5$ into our formula.
It's like plugging in a special code to unlock a secret number!

STEP 4

Substituting $n = 5$ into the formula gives us: $T(5) = (5)^2 + 3$ Remember, $T(5)$ just means the value of the term when $n$ is 5.

STEP 5

Now, we need to evaluate this expression.
First, we deal with the exponent: $(5)^2 = 5 \cdot 5 = 25$ So, we have: $T(5) = 25 + 3$

STEP 6

Finally, we add $25$ and $3$ together: $25 + 3 = 28$ So, $T(5) = 28$ .
Awesome!

STEP 7

The 5th term of the sequence is $\textbf{28}$ .

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QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+3$
Work out the $5^{\text {th }}$ term of this sequence.

Studdy Solution

STEP 1

What is this asking? Given a formula that tells us the value of any term in a sequence, we need to find the value of the 5th term. Watch out! Make sure to substitute the correct value for $n$ and follow the order of operations (PEMDAS/BODMAS) carefully!

STEP 2

1. Substitute and Evaluate

STEP 3

Alright, let's dive in!
We've got this awesome formula $T(n) = n^2 + 3$ that tells us the value of the $n$ th term in a sequence.
We want to find the 5th term, so we're going to substitute $n = 5$ into our formula.
It's like plugging in a special code to unlock a secret number!

STEP 4

Substituting $n = 5$ into the formula gives us: $T(5) = (5)^2 + 3$ Remember, $T(5)$ just means the value of the term when $n$ is 5.

STEP 5

Now, we need to evaluate this expression.
First, we deal with the exponent: $(5)^2 = 5 \cdot 5 = 25$ So, we have: $T(5) = 25 + 3$

STEP 6

Finally, we add $25$ and $3$ together: $25 + 3 = 28$ So, $T(5) = 28$ .
Awesome!

STEP 7

The 5th term of the sequence is $\textbf{28}$ .

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QuestionThe nth n^{\text {th }}nth term rule for a sequence is T(n)=n2+3T(n)=n^{2}+3T(n)=n2+3Work out the 5th 5^{\text {th }}5th term of this sequence.

Studdy Solution

STEP 1

What is this asking? Given a formula that tells us the value of any term in a sequence, we need to find the value of the 5th term. Watch out! Make sure to substitute the correct value for nnn and follow the order of operations (PEMDAS/BODMAS) carefully!

STEP 2

1. Substitute and Evaluate

STEP 3

STEP 4

Substituting n=5n = 5n=5 into the formula gives us: T(5)=(5)2+3T(5) = (5)^2 + 3T(5)=(5)2+3 Remember, T(5)T(5)T(5) just means the value of the term when nnn is **5**.

STEP 5

Now, we need to **evaluate** this expression.First, we deal with the exponent: (5)2=5⋅5=25(5)^2 = 5 \cdot 5 = 25(5)2=5⋅5=25 So, we have: T(5)=25+3T(5) = 25 + 3T(5)=25+3

STEP 6

Finally, we add 252525 and 333 together: 25+3=2825 + 3 = 2825+3=28 So, T(5)=28T(5) = 28T(5)=28.Awesome!

STEP 7

The 5th term of the sequence is 28\textbf{28}28.

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QuestionThe $n^{\text {th }}$ term rule for a sequence is $T(n)=n^{2}+3$
Work out the $5^{\text {th }}$ term of this sequence.

What is this asking? Given a formula that tells us the value of any term in a sequence, we need to find the value of the 5th term. Watch out! Make sure to substitute the correct value for $n$ and follow the order of operations (PEMDAS/BODMAS) carefully!

Substituting $n = 5$ into the formula gives us: $T(5) = (5)^2 + 3$ Remember, $T(5)$ just means the value of the term when $n$ is 5.

Now, we need to evaluate this expression.
First, we deal with the exponent: $(5)^2 = 5 \cdot 5 = 25$ So, we have: $T(5) = 25 + 3$

Finally, we add $25$ and $3$ together: $25 + 3 = 28$ So, $T(5) = 28$ .
Awesome!

The 5th term of the sequence is $\textbf{28}$ .