Question

The $8^{\text{th}}$ term of the sequence 1, 1, 2, 3, 5, 8….. is
A) 25
B) 24
C) 23
D) 21

Answer 1

We have to find the $8^{\text{th}}$ term of this sequence. This sequence is actually known as Fibonacci sequence as each of the terms in this sequence is the sum of the last two terms.
Total six terms are given in this sequence, so to calculate the $8^{\text{th}}$ term, we will first calculate the $7^{\text{th}}$ term of this sequence. The $7^{\text{th}}$ term of this sequence is equal to the sum of the $5^{\text{th}}$ term and the $6^{\text{th}}$ term. After calculating $7^{\text{th}}$, we will calculate $8^{\text{th}}$ term by adding $6^{\text{th}}$ term and $7^{\text{th}}$ term of this sequence. After addition, we will get the required $8^{\text{th}}$ term.

Complete step by step solution:
Given sequence is
1, 1, 2, 3, 5, 8…..
This sequence is known as Fibonacci sequence as each of its terms is equal to the sum of the last two terms.
We have to calculate the $8^{\text{th}}$ term of this sequence.
First we will calculate the $7^{\text{th}}$ term of this sequence, which will be equal to the sum of $5^{\text{th}}$ term and $6^{\text{th}}$ term.
${{7}^{th}}\text{term}={{5}^{th}}\text{term}+{{6}^{th}}\text{term}$ …………..$(1)$
The $5^{\text{th}}$ term of this sequence is 5 and the $6^{\text{th}}$ term of this sequence is 8.
Now, we will put the value of $5^{\text{th}}$ and $6^{\text{th}}$ term in equation $(1)$
${{7}^{th}}\text{term}=5+8=13$
Therefore, the $7^{\text{th}}$ term of this sequence is 13.
Now, we will calculate the value of the $8^{\text{th}}$ term, which will be equal to the sum of $6^{\text{th}}$ term and $7^{\text{th}}$ term.
${{8}^{th}}\text{term}={{6}^{th}}\text{term}+{{7}^{th}}\text{term}$ …………..$(2)$
The $6^{\text{th}}$ term of this sequence is 8 and the $7^{\text{th}}$ term of this sequence is 13.
Now, we will put the value of $6^{\text{th}}$ and $7^{\text{th}}$ term in equation $(2)$
${{8}^{th}}\text{term}=8+13=21$
Therefore, the $8^{\text{th}}$ term of this sequence is 21.

Thus, the correct option is D.

Note:
We have used the Fibonacci sequence here which is defined as a sequence which starts with either 1 or 0 and each term of the sequence is equal to the sum of the preceding two terms.
Fibonacci sequence is named after one Italian mathematician, Fibonacci. This is widely used in mathematics, science and computers.