The second term of arithmetic progression is 15 and the fifth term is 21 find the common difference with solutions
_ 15 _ _ 21
What do you think?
To find the common difference in an arithmetic progression (AP), we need to observe the pattern in the given terms.
An AP is a sequence of numbers in which the difference between any two consecutive terms is constant. Let's label the second term as a and the common difference as d.
Given:
Second term (a2) = 15
Fifth term (a5) = 21
In an arithmetic progression, the nth term (an) is given by the formula:
an = a + (n-1)d
We know a2 = 15, which means the second term is a + d.
So, a2 = a + d
15 = a + d ----(1)
Similarly, we know a5 = 21, which can be expressed as:
a5 = a + 4d
21 = a + 4d ----(2)
We now have a system of equations, (1) and (2), which can be solved simultaneously to determine the values of a and d.
From equation (1), we can express 'a' in terms of 'd':
a = 15 - d
Substituting this value for 'a' in equation (2), we get:
21 = (15 - d) + 4d
21 = 15 + 3d
6 = 3d
d = 2
Hence, the common difference (d) is 2.