Question

Write the nth term of an A.P. the sum of whose n terms is Sn.

A) Tn = Sn - Sn-1
B) Tn = n(Sn - Sn-1)
C) Tn = 2Sn - Sn-1
D) Tn = Sn

Answer 1

The nth term of an arithmetic progression (A.P.) can be found using the formula Tn = a + (n-1)d, where a is the first term and d is the common difference. The sum of an A.P. up to the nth term (Sn) can be found using the formula Sn = (n/2)(2a + (n-1)d). To find the nth term of an A.P. given the sum of its n terms (Sn), rearrange the formula for Sn and solve for Tn.

Step-by-step explanation:

The nth term of an arithmetic progression (A.P.) can be found using the formula Tn = a + (n-1)d, where a is the first term and d is the common difference.

The sum of an A.P. up to the nth term (Sn) can be found using the formula Sn = (n/2)(2a + (n-1)d).

So, to find the nth term of an A.P. given the sum of its n terms (Sn), we can rearrange the formula for Sn and solve for Tn.

Let's write out the steps:

1. Start with the formula for Sn: Sn = (n/2)(2a + (n-1)d)
2. Rearrange the formula: Sn = (n/2)(2a) + (n/2)(n-1)d
3. Note that the first term (a) is the same as T1, so we can rewrite the formula as: Sn = n(a) + (n/2)(n-1)d
4. Simplify the equation: Sn = nT1 + (n/2)(n-1)d
5. Now, solve for T1 by subtracting the second term from both sides of the equation: Sn - (n/2)(n-1)d = nT1
6. Divide both sides by n to find the value of T1: T1 = (Sn - (n/2)(n-1)d)/n

Therefore, the nth term of an A.P. when the sum of its n terms is Sn is given by the formula: Tn = (Sn - (n/2)(n-1)d)/n