If the general term of an A. P. Is Tn =(3n-7) find the first term and common difference of A. P.
To find the first term and common difference of an arithmetic progression (A.P.) given its general term, Tn, we can equate Tn with the given expression and solve for the values.
The general term of an A.P. is given by the formula Tn = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
In this case, we are given that Tn = 3n - 7. We can substitute this into the general term formula and solve for 'a' and 'd'.
So, the equation becomes:
3n - 7 = a + (n-1)d
To find the first term, we need to find the value of 'a'. We can do this by substituting any value for 'n' in the equation and solving for 'a'. Let's choose n = 1.
When n = 1, the equation becomes:
3(1) - 7 = a + (1-1)d
3 - 7 = a
-4 = a
Hence, the first term (a) of the A.P. is -4.
To find the common difference, we can use the equation above. Let's use n = 2 this time:
3(2) - 7 = a + (2-1)d
6 - 7 = a + d
-1 = -4 + d
d = -1 - (-4)
d = -1 + 4
d = 3
Therefore, the common difference (d) of the A.P. is 3.
In summary, given the general term Tn = 3n - 7, the first term (a) of the A.P. is -4 and the common difference (d) is 3.