Question

Calculate the value of the ${12}^{th}$ and the ${13}^{th}$ term of the Fibonacci sequence given that the $9^{th}$ and ${10}^{th}$ terms in the sequence are 21 and 34.

• A. 89 and 140
• B. 89 and 146
• C. 88 and 144
• D. 89 and 144

Answer 1

The correct option is D 89 and 144

Using the Fibonacci sequence formula, we can say that the ${11}^{th}$ term is the sum of $9^{th}$ term and ${10}^{th}$ term.
${11}^{th}$ term = $9^{th}$ term + ${10}^{th}$ term = 21 + 34 = 55
Now, ${12}^{th}$ term = ${10}^{th}$ term + ${11}^{th}$ term = 34 + 55 = 89
Similarly, ${13}^{th}$ term = ${11}^{th}$ term + ${12}^{th}$ term = 55 + 89 = 144
The ${12}^{th}$ and the ${13}^{th}$ term of the Fibonacci sequence are 89 and 144.