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Write the set B={a(n):n in N,a(n+2)=a(n+...

Write the set `B={a_(n):n in N,a_(n+2)=a_(n+1)+a_(n)anda_(1)=a_(2)=1}` in tabular form.

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To write the set \( B = \{ a_n : n \in \mathbb{N}, a_{n+2} = a_{n+1} + a_n, a_1 = a_2 = 1 \} \) in tabular form, we will follow these steps: ### Step-by-Step Solution: 1. **Identify the Initial Conditions:** - We know that \( a_1 = 1 \) and \( a_2 = 1 \). 2. **Use the Recurrence Relation:** - The recurrence relation given is \( a_{n+2} = a_{n+1} + a_n \). We will use this to find subsequent terms. 3. **Calculate \( a_3 \):** - Using the relation for \( n = 1 \): \[ a_3 = a_2 + a_1 = 1 + 1 = 2 \] 4. **Calculate \( a_4 \):** - Using the relation for \( n = 2 \): \[ a_4 = a_3 + a_2 = 2 + 1 = 3 \] 5. **Calculate \( a_5 \):** - Using the relation for \( n = 3 \): \[ a_5 = a_4 + a_3 = 3 + 2 = 5 \] 6. **Calculate \( a_6 \):** - Using the relation for \( n = 4 \): \[ a_6 = a_5 + a_4 = 5 + 3 = 8 \] 7. **Continue the Pattern:** - We can continue this process to find more terms if needed, but for the purpose of the set, we will stop here. 8. **Write the Set in Tabular Form:** - Now we can write the values we calculated in a tabular format: \[ \begin{array}{|c|c|} \hline n & a_n \\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 2 \\ 4 & 3 \\ 5 & 5 \\ 6 & 8 \\ \vdots & \vdots \\ \hline \end{array} \] - The set \( B \) can be expressed as: \[ B = \{ 1, 1, 2, 3, 5, 8, \ldots \} \]
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