Question

Find the missing terms in the AP:18,_,8,_

Answer 1

Given :-

AP = 18 , _ , 8 , _

Required to find :-

• Missing terms

Formula used :-

$\large{ \leadsto{ \boxed{ \tt{{a}_{nth} = a + (n - 1)d}}}}$

Solution :-

Given data :-

AP = 18 , _ , 8 , _

we need to find the missing terms .

The terms which are missing are ;

• 2nd term

• 4th term

However,

The terms which are given are ; 1st term & 3rd term .

So,

We know that ;

• First term ( a ) = 18

Third term = 8

But,

Third term can be represented as ; a + 2d

=> a + 2d = 8 $\longrightarrow{\tt{ Equation - 1 }}$

consider this as equation - 1

Now,

Let's find the value of d

So, substitute the value of a in eq 1

a + 2d = 8

18 + 2d = 8

2d = 8 - 18

2d = - 10

d = -10/2

d = - 5

Hence,

• Common difference ( d ) = - 5

Now let's find the 2nd , 4th term

Using the formula ;

$\large{\dagger{\boxed{\rm{ {a}_{nth} = a + ( n - 1 ) d }}}}$

$\rightarrow{\rm{ {a}_{nth} = {a}_{2} }}$

$\rightarrow{\rm{ {a}_{2} = 18 + ( 2 - 1 ) - 5 }}$

$\rightarrow{\rm{ {a}_{2} = 18 + ( 1 ) - 5 }}$

$\rightarrow{\rm{ {a}_{2} = 18 - 5 }}$

$\rightarrow{\rm{ {a}_{2} = 13 }}$

Hence,

2nd term = 13

Similarly,

$\rightarrow{\rm{ {a}_{nth} = {a}_{4} }}$

$\rightarrow{\rm{ {a}_{4} = 18 + ( 4 - 1 ) - 5 }}$

$\rightarrow{\rm{ {a}_{4} = 18 + ( 3) - 5 }}$

$\rightarrow{\rm{ {a}_{4} = 18 - 15 }}$

$\rightarrow{\rm{ {a}_{4} = 3 }}$

Hence,

4th term = 3

Therefore ,

The missing terms of the AP are ; 13 & 3

So,

Atlast the AP is ;

AP = 18 , 13 , 8 , 3