Question

Four numbers are inserted between the numbers 4 and 39 such that an A.P. results.The greatest of these 4 numbers is

a) 31
b) 32
c) 33
d) 30
e) Option 5

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Answer 1

Answer:

b). 32

Solution:

★ Let the first number be a and second number be b .

Here,

a = 4 and b = 39

★ Now , find the common difference d using the formula , d = (b - a)/(n + 1) , where n is the number of AMs between a and b .

Here ,

=> d = (b - a)/(n + 1)

=> d = (39 - 4)/(4 + 1)

=> d = 35/5

=> d = 7

★ In general , the nth AM is given as (a + nd)

→ Now , the AMs between a and b will be given as ;

• 1st AM = a + d = 4 + 7 = 11

• 2nd AM = a + 2d = 4 + 2×7 = 4 + 14 = 18

• 3rd AM = a + 3d = 4 + 3×7 = 4 + 21 = 25

• 4th AM = a + 4d = 4 + 4×7 = 4 + 28 = 32

Hence ,

The 4 AMs between 4 and 39 are :

11 , 18 , 25 , 32 .

Clearly ,

Among all these four AMs , 32 is the greatest .

Hence ,

Required answer is 32 .