Question

In an A.P. tp=q , tq=p. Show that tm=p+q-m

Answer 1

Answer :

Let us take that the first term of the AP is a and the common difference is d

Given that,

$t_p$ = q

⇨ a + (p - 1)d = q ...(i)

and

$t_q$ = p

⇨ a + (q - 1)d = p ...(ii)

Now, (i) - (ii) ⇨

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

⇨ (p - 1 - q + 1)d = q - p

⇨ (p - q)d = - (p - q)

⇨ d = - 1

Now, putting d = - 1 in (i), we get

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

⇨ a = p + q - 1

Hence, the m-th term be

$t_m$

= a + (m - 1)d

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

= p + q - 1 - m + 1

= p + q - m

Hence, proved.

#MarkAsBrainliest

Answer 2

#ANSWERWITHQUALITY

#BAL

Answer:

Hey frnd ❤️

Here is your answer

pls refer to the attachment