THE FRIST TERM OF AN A.P IS EQUAL TO TWICE THE COMMON DIFFERENCE D FIND IN TERM OF D THE 5TH TERM OF THE A.P
The frist term of an A.P is equal to twice the common difference d mean:
a1 = 2 d
nth term of the A.P:
an = a1 + ( n - 1 ) d
a5 = a1 + ( 5 - 1 ) d
a5 = a1 + 4 d
Since a1 = 2 d
a5 = a1 + 4 d = 2 d + 4 d = 6 d
a5 = 6 d
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To find the 5th term of an arithmetic progression (A.P.) in terms of the common difference (d), we need to understand the A.P. formula and the given condition.
Let's start by understanding the basics:
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is denoted by 'd'.
Now, let's consider the given condition:
The first term (a1) of the arithmetic progression is equal to twice the common difference (d): a1 = 2d.
To find the 5th term (a5) of the A.P., we'll use the formula:
an = a1 + (n-1)d,
where 'an' is the nth term of the A.P., 'a1' is the first term, 'n' is the position of the term, and 'd' is the common difference.
Substituting the given values into the formula:
a5 = a1 + (5-1)d.
Since the first term (a1) is given as 2d, we substitute it into the equation:
a5 = 2d + (5-1)d.
Simplifying the equation:
a5 = 2d + 4d.
Combining like terms:
a5 = 6d.
Therefore, the 5th term of the arithmetic progression, in terms of the common difference (d), is 6d.