Question

the pth term of an AP is q and the qth term is p, prove that its nth term is (p + q --n).​

Answer 1

Step-by-step explanation:

This night is cold in the kingdom

I can feel you fade away

From the kitchen to the bathroom sink and

Your steps keep me awake

Don't cut me down, throw me out, leave me here to waste

I once was a man with dignity and grace

Now I'm slippin' through the cracks of your cold embrace

So please, please

Could you find a way to let me down slowly?

A little sympathy, I hope you can show me

If you wanna go then I'll be so lonely

If you're leavin', baby, let me down slowly

Let me down, down, let me down, down, let me down

Let me down, down, let me down, down, let me down

If you wanna go then I'll be so lonely

If you're leavin', baby, let me down slowly

Cold skin, drag my feet on the tile

As I'm walking down the corridor

And I know we haven't talked in a while

So I'm looking for an open door

Don't cut me down, throw me out, leave me here to waste

I once was a man with dignity and grace

Now I'm slippin' through the cracks of your cold embrace

So please, please

Could you find a way to let me down slowly?

A little sympathy, I hope you can show me

If you wanna go then I'll be so lonely

If you're leavin', baby, let me down slowly

Let me down, down, let me down, down, let me down

Let me down, down, let me down, down, let me down

If you wanna go then I'll be so lonely

If you're leavin', baby, let me down slowly

And I can't stop myself from fallin' (down) down

And I can't stop myself from fallin' (down) down

And I can't stop myself from fallin' (

Answer 2

As we know the Pth term of an AP is Q.

• → Tₚ = q
• → a + (p - 1)d = q ...[1]

Qth term of an AP is P.

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

Now, If we will Equalise both the EQUATIONS so we'll found that;

→ (p -1)d – (q - 1)d = (q - p)

→ pd - d - qd + d = (q - p)

→ pd - qd = (q - p)

→ -d(q - p) = (q - p)

→ -d = 1

→ d = –1

†We're going to find the FIRST TERM of an AP using the value of common Difference.

→ a + (p - 1)d = q

→ a - (p - 1) = q

→ a = q + (p - 1)

→ a = (q + p - 1)

Finally, It's time to PROVE that nth term will be (p + q - n).

→ Tₙ = a + (n - 1)d

→ Tₙ = (q + p - 1) + (n - 1)(-1)

→ Tₙ = (q + p - 1) - (n - 1)

→ Tₙ = q + p - 1 - n + 1

→ Tₙ = (q + p - n)