Question

the 7th tern and the 17th tern of an A.p. are 24 and 54 respectively. find the 12th tern of this A.p.​

Answer 1

$\bf\red{QuestioN:-}$

The 7th term and the 17th term of an AP are 24 and 54 respectively. Find the 12th term of this AP.​

$\bf\purple{AnsweR:-}$

7th term of an AP is given as 24.

That is,

a + 6d = 24

17th term of that AP is given as 54.

That is,

a + 16d = 54

On comparing both these terms,

a + 6d = 24 ------ [ Eq.1]

a + 16d = 54 -------[Eq.2]

[eq.2] - [eq.1]

$\pink:\implies\tt{(a+16d)-(a+6d)=54-24}$

$\pink:\implies\tt{(10d)=30}$

$\pink:\implies\tt{d=\dfrac{30}{10}}$

$\pink:\implies\tt{d=3}$

Then the common difference is 3.

Now we can substitute d in Eq.1.

$\green:\implies\tt{(a+6d)=24}$

$\green:\implies\tt{(a+6\times3)=24}$

$\green:\implies\tt{(a+18)=24}$

$\green:\implies\tt{a=24-18}$

$\green:\implies\tt{a=6}$

According to this,

The 12th term of this AP will be,

a + 11d

We already know the values a and d.

On substituting the values,

• a + 11 d,

• 6 + 11 × 3

• 6 + 33

• 39

All Done!!☺