Question

How to find the eleventh and sixth term of an A. P are 48 and 23. Calculate the first term and the common difference

Answer 1

To find the first term and the common difference of an arithmetic progression (A.P.), we can use the formulas:

nth term (Tn) = a + (n - 1)d

Where Tn represents the nth term, a represents the first term, n represents the position of the term in the A.P., and d represents the common difference.

Given that the eleventh term (T11) is 48 and the sixth term (T6) is 23, we can set up the following equations:

T11 = a + (11 - 1)d
48 = a + 10d

T6 = a + (6 - 1)d
23 = a + 5d

Now we have a system of two equations with two variables. We can solve it by substitution or elimination method.

Using the elimination method, we can subtract the second equation from the first equation to eliminate the "a" term:

48 - 23 = (a + 10d) - (a + 5d)
25 = 5d
d = 25/5
d = 5

Now that we have found the common difference (d) to be 5, we can substitute this value back into one of the equations to find the first term (a).

23 = a + 5(5)
23 = a + 25
a = 23 - 25
a = -2

Therefore, the first term (a) of the A.P. is -2, and the common difference (d) is 5.