The 2nd term and 5th term of an a.p are 2/3 and 1/12, respectively find the first term?
the terms are 3 apart, so
3d = 1/12 - 2/3 = -7/12
d = -7/36
so a = 2/3 - (-7/36) = 31/36
a + d(n-1)
2nd = a + d = 2/3
5th = a + 4d =1/12
To find the first term of an arithmetic progression (AP), you need to know the common difference between the terms and at least two terms from the sequence. In this case, we are given the second term and the fifth term.
Let's label the first term of the AP as "a" and the common difference as "d." Then, we can use the following formulas:
Second term (T2) = a + d
Fifth term (T5) = a + 4d
We are given that the second term (T2) is 2/3 and the fifth term (T5) is 1/12. Substituting these values into the formulas, we get:
2/3 = a + d ...(equation 1)
1/12 = a + 4d ...(equation 2)
Now, we need to solve these two equations simultaneously to find the values of "a" and "d."
First, let's eliminate the variable "a" by multiplying equation 1 by 4:
8/3 = 4a + 4d ...(equation 3)
Next, subtract equation 2 from equation 3 to eliminate the variable "a":
8/3 - 1/12 = 4a + 4d - (a + 4d)
(32/12) - (1/12) = 3a
(31/12) = 3a
Now, divide both sides by 3 to find the value of "a":
31/12 รท 3 = a
31/36 = a
Therefore, the first term (a) of the arithmetic progression is 31/36.