insert two A.M between 3/2 and 27/14
Answers
Step-by-step explanation:
a
1
=2
a
5
=14
n=5
d=?
a
n
=a+(n−1)d
a
5
=a+(5−1)d
14=2+4d
12=4d
d=3
∴2,5,8,11,14
Answer:
15/14 and 9/14.
Step-by-step explanation:
To find the two arithmetic means (A.M.) between 3/2 and 27/14, we can use the formula for the nth term of an arithmetic sequence:
An = A + (n - 1) * d
Where An is the nth term, A is the first term, n is the term number, and d is the common difference.
Given the first term A1 = 3/2 and the fifth term A5 = 27/14, we can set up the equations:
A2 = A1 + d
A3 = A2 + d
Substituting the values, we have:
A1 + d = 3/2
A1 + 2d = 27/14
Simplifying the equations:
A1 + d = 3/2
A1 + 2d = 27/14
Subtracting the first equation from the second equation, we get:
d = 27/14 - 3/2
d = 27/14 - 21/14
d = 6/14
d = 3/7
Now we can substitute the value of d back into the first equation to find A1:
A1 + (3/7) = 3/2
A1 = 3/2 - 3/7
A1 = 21/14 - 6/14
A1 = 15/14
Therefore, the two arithmetic means between 3/2 and 27/14 are 15/14 and 9/14.