If the first term of an AP is equal to one-half of the common difference d.find the 8th term of the AP
(8 d / 2) + (7/2 * 8 d) = 32 d
First term is =3/2
Eight term= a+(n-1)d
a=3/2
3/2+8-1*d
3/2+7d
LCM =2
= 3d+14/2
=17d
Let's start by using the formula for the nth term of an arithmetic progression (AP):
a_n = a_1 + (n-1) * d
where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.
In this case, the first term (a_1) is equal to one-half of the common difference (d), so we have:
a_1 = 1/2 * d
Now, we need to find the 8th term (a_8). Plugging in the values into the formula:
a_8 = (1/2 * d) + (8-1) * d
Simplifying this equation:
a_8 = (1/2 * d) + 7 * d
Combining the terms:
a_8 = (1/2 + 7) * d
a_8 = (15/2) * d
So, the 8th term of the arithmetic progression is (15/2) * d.
To find the 8th term of an arithmetic progression (AP), we need to know the first term and the common difference.
Let's label the first term of the AP as "a" and the common difference as "d."
Given that the first term is equal to one-half of the common difference, we can write the equation: a = 1/2 * d.
To find the value of a, we need to know the value of d. Unfortunately, the problem does not provide that information.
However, we can still calculate the 8th term if we have a value for either a or d. Let's solve for the 8th term in terms of d:
The nth term formula for an AP is given by: an = a + (n - 1)*d
Substituting a = 1/2 * d and n = 8, we get:
a8 = (1/2 * d) + (8 - 1)*d
a8 = (1/2 * d) + 7d
a8 = (1/2 + 7)*d
a8 = (15/2)*d
So, the 8th term of the AP is (15/2)*d, where d is the common difference.