Step-by-step explanation:

GIVEN :-

4, a , b, c , 28 are in AP

To find:-

Find the value of c ?

Solution :-

General Method:-

Given that :

4, a , b, c , 28 are in AP

FIRST term ( a ) = 4

Fifth term (a 5)= 28

We know that

nth term of an AP is an = a+(n-1) d

=> a 5 = a+(5-1)d

=> a 5 = a+4d

=> a+4d = 28

=> 4+4d = 28

=> 4d = 28-4

=> 4d = 24

=> d = 24/4

=> d = 6

Common difference = 6

Now,

c is the fourth term

=> a 4 = a+3d

=> c = 4+3(6)

=> c = 4+18

=>c = 22

Therefore, c = 22

Alternative Method:-

Given that

4, a , b, c , 28 are in AP

We know that

If 'n' AM's are between a and b then d = (b-a)/(n+1)

We have , a = 4, b = 28 ,n = 3

Since a,b,c are between 4 and 28

=> d = (28-4)/(3+1)

=>d = 24/4

=> d = 6

c is the fourth term

=> a 4 = a+3d

=> c = 4+3(6)

=> c = 4+18

=>c = 22

Therefore, c = 22

Answer:-

The value of c for the given problem is 22

Used formulae:-

• nth term of an AP is an = a+(n-1) d
• If 'n' AM's are between a and b then d = (b-a)/(n+1)
• a = First term
• b = last term
• d = Common difference
• n = Number of terms
• AM = Arithmetic Mean
• AP = Arithmetic PROGRESSION