The first term a of an A.P. is equal to twice the common difference d.find, in terms of d, the fifth term of the A.P.
The nth term of an arithmetic progression is given by the formula:
an = a + (n-1)d
Given that the first term a is equal to twice the common difference, i.e. a = 2d, we can substitute this value into the formula:
an = 2d + (n-1)d
an = 2d + dn - d
an = d(2 + n) - d
an = d(n+1)
To find the fifth term of the A.P., we substitute n = 5 into the formula:
a5 = d(5+1)
a5 = d(6)
a5 = 6d
Therefore, the fifth term of the A.P. in terms of the common difference d is 6d.