Insert two numbers between 3 and 24 such that the resulting sequence is an A.P.
Please help fast!
Answers
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.
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
∴ x = 3 + 7 = 10
∴ y = 3 + 14 = 17
FINAL ANSWER
Hence the required two numbers are 10 and 17
━━━━━━━━━━━━━━━━
Learn more from Brainly :-
1. the sum of the third and seventh term of an AP is 40 and the sum sixth and 14th terms is 70 .Find the sum of first ten
https://brainly.in/question/22811954
2. find the 100th term of an AP whose nth term is 3n+1
https://brainly.in/question/22293445