Question

Insert two numbers between 3 and 24 such that the resulting sequence is an A.P.

Please help fast!

Answer 1

Given,

The first and last terms are = 3 and 24

To find,

The second and third terms of the AP

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the common difference = x

Second term = 3+x

Third term = 3+x+x = 3+2x

Fourth term = 3+2x+x = 3+3x

According to the data mentioned in the question,

3+3x = 24

3(1+x) = 3×8

1+x = 8

x = 7

Second term = 3+7 = 10

Third term = 10+7 = 17

Hence, 10 and 17 will create an AP series.

Answer 2

SOLUTION

TO DETERMINE

Insert two numbers between 3 and 24 such that the resulting sequence is an A.P.

EVALUATION

We have to Insert two numbers between 3 and 24 such that the resulting sequence is an A.P.

Let x , y be the two numbers

Then 3 , x , y , 24 forms an arithmetic progression

Let d be the Common Difference

Then

x = 3 + d

y = 3 + 2d

24 = 3 + 3d

Now 24 = 3 + 3d gives

3d = 21

$\implies \sf{d = 7}$

∴ x = 3 + 7 = 10

∴ y = 3 + 14 = 17

FINAL ANSWER

Hence the required two numbers are 10 and 17

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