Work out the nth term rule for the given sequence 20, 21, 22, 23, 24...a) nth term rule is b) What is the 25th term in the given sequence.

1. Break Down the Problem

To find the nth term rule for the sequence 20, 21, 22, 23, 24, we first observe the pattern and then express it in a formula. After determining the nth term rule, we will calculate the 25th term.

2. Relevant Concepts

The sequence is an arithmetic sequence, which can generally be expressed as: $a_n = a + (n - 1) \cdot d$ where:

• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the term number.

3. Analysis and Detail

1. Identify $a$ (the first term): $a = 20$

2. Identify $d$ (the common difference):

   • The difference between consecutive terms is $1$ (for example, $21 - 20 = 1$). $d = 1$

3. Construct the nth term formula: Substituting $a$ and $d$ into the nth term formula: $a_n = 20 + (n - 1) \cdot 1$ Simplifying this gives: $a_n = 20 + n - 1 = n + 19$

4. Verify and Summarize

To verify, substitute $n = 1$ to check if $a_1 = 20$: $a_1 = 1 + 19 = 20 \quad \text{(correct)}$ Now substitute $n = 2$: $a_2 = 2 + 19 = 21 \quad \text{(correct)}$ This confirms the formula works for the initial terms.

Final Answer

a) The nth term rule is: $a_n = n + 19$

b) To find the 25th term, substitute $n = 25$: $a_{25} = 25 + 19 = 44$ The 25th term in the given sequence is 44.