If the first term of an AP is equal to one_half of the common difference,d,find the 8th term of the AP
Let the first term of the AP be a and the common difference be d.
According to the given condition, a = (1/2)d.
The formula for the nth term of an AP is: an = a + (n-1)d.
We want to find the 8th term, so n = 8.
8th term, a8 = a + (8-1)d = a + 7d.
Substituting the value of a from the given condition:
a8 = (1/2)d + 7d
Combining the fractions:
a8 = (1/2)d + (14/2)d
a8 = (15/2)d
Therefore, the 8th term of the AP is (15/2)d.
Let's denote the first term of the arithmetic progression (AP) as a₁ and the common difference as d.
According to the given information, the first term, a₁, is equal to one-half of the common difference, d. Mathematically, we can represent this as:
a₁ = (1/2) * d
To find the 8th term of the AP, we can use the formula for the nth term of an AP:
aₙ = a₁ + (n-1) * d
Substituting the value of a₁ in terms of d, we can rewrite the formula as:
aₙ = (1/2) * d + (n-1) * d
Now, let's substitute n = 8 into the formula to find the 8th term:
a₈ = (1/2) * d + (8-1) * d
Simplifying,
a₈ = (1/2) * d + 7d
Now, we can find the 8th term of the AP by simplifying the expression above.
To find the 8th term of an arithmetic progression (AP) when the first term is equal to half of the common difference, you need to know the value of the common difference, denoted as 'd'. Let's denote the first term as 'a' and the term to be found as 't[8]'.
Given:
First term, a = 1/2d
Now let's use the formula to find the nth term of an AP:
t[n] = a + (n-1)d
To find the 8th term, substitute the values into the formula:
t[8] = (1/2d) + (8-1)d
Simplify the equation:
t[8] = (1/2d) + 7d
To combine the terms with different denominators, find a common denominator:
t[8] = (1/2d) + (7d*2/2)
t[8] = (1 + 14d)/2d
Thus, the 8th term of the AP is (1 + 14d)/2d.