Question

In an AP Tp = q , Tq = p find Sp+q​

Answer 1

Answer:

This is the answer of this question

Answer 2

$S_{p + q} = \frac{1}{2}(p + q)(p + q - 1)$

Step-by-step explanation:

Let the first term of the A.P. is a and the common difference is d.

So, [a + (p - 1)d] = q ............. (1) and

[a + (q - 1)d] = p ............... (2)

Now, subtracting equation (2) from equation (1), we get

(p - 1 - q + 1)d = q - p

⇒ (p - q)d = q - p

⇒ d = - 1 {As p ≠ q}

So, from equation (2) we get,

a - (q - 1) = p

⇒ a = p + q - 1

Now, Sum of (p + q) terms = $S_{p + q} = \frac{p + q}{2}[2a + (p + q - 1)d]$

= $\frac{p + q}{2}[2(p + q - 1) + (p + q - 1)(- 1)]$

= $\frac{1}{2}(p + q)(p + q - 1)$ (Answer)