Question

If the pth term of an A.P. is q and qth term is p , show that its (p+q)th term is 0​

Answer 1

Answer:

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Assume a be first term

★Common Difference be d

★Hence,

${\boxed{\sf\:{a_{p}=q}}}$

${\boxed{\sf\:{a_{q}=p}}}$

a + (p - 1)d = q ……. (1)

a + (q - 1)d = p ……..(2)

$\large{\fbox{Subtracting equations we get}$

(p - q)d = q - p

d = -1

$\large{\fbox{Substitute the value of d in eq (1)}$

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

a = (p + q - 1)

${\boxed{\sf\:{a_{p+q}=a+(p+q-1)d}}}$

$\large\fbox{Substitute the value of d we get}$

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

= 0

$\Large{\fbox{Hence Proved}}$