Question

In the sequence- $a,b,c,d,0,1,1,2,3,5,8........$ each term is the sum of the two terms to its left. Find $a$
$A)-3$
$B)-1$
$C)0$
$D)1$

Answer 1

Hint: To solve this question we need to have knowledge of Arithmetic Operation. In this question we will solve the value of $a$ . For this we will solve by calculating the value of “d” then “c” then “b” and lastly “a”. These values will be solved keeping in mind the condition of the sequence, which says each term is the sum of the two terms to its left.

Complete step by step answer:
The question ask us to find the value of “a” when a sequence of given numbers with$a,b,c,d,0,1,1,2,3,5,8........$, when in the question it given that each term is the sum of the two terms to its left. The first step is to calculate the value $d$. To calculate the value of $d$ we will write the sum of $d$ and $0$ as $1$. Mathematically it will be represented as:
$\Rightarrow d+0=1$
On calculating further the value of $d$ is:
$\Rightarrow d=1$
The next step is to find the value of “c”. Again we will apply the same condition which says that each term is the sum of the two terms to its left. On calculating we get:
$\Rightarrow c+d=0$
Substituting the value of $d$ as $1$ we get:
$\Rightarrow c+1=0$
$\Rightarrow c=-1$
The third step is to find the value $b$by working in the same process and same condition. So on applying the same condition we get:
 $\Rightarrow b+c=d$
Since we know that the values of $c$ and $d$ are given. So we will be substituting the values we got in the two unknown which are $c$ and $d$. On doing so we get:
$\Rightarrow b-1=1$
$\Rightarrow b=1+1$
$\Rightarrow b=2$
Now comes the last step in which we are supposed to find the value of $a$. Applying the same condition we get:
$\Rightarrow a+b=c$
On substituting the values of $b$ and $c$, we get:
$\Rightarrow a+2=-1$
$\Rightarrow a=-1-2$
$\Rightarrow a=-3$

So, the correct answer is “Option A”.

Note: We can check whether the answer is correct or not. For this we will add the terms on the left and check whether the sum satisfies the condition or not. To start with adding $a$ and $b$. On doing this we get:
$\Rightarrow a+b=c=-3+2=-1$
The next step is to add $c$ and $d$and check whether the sum is $0$ or not. On adding we get:
$\Rightarrow c+d$
$\Rightarrow -1+1=0$
Since the sum is zero, the answer we got is correct.