Question

can someone please tell me how to solve the circled question

Answer 1

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Let the first term be a0
let the common difference be d
pth term = a0 +(p-1)d
=> q = a0 + (p-1)d .................................... (1)
qth term = a0 + (q-1)d
=> p = a0 + (q-1)d ....................................(2)
Subtracting (1) from (2)
q-p=(p-q)d
=>d = -1
putting the value of d in (1),we get
a0 = q+p-1
therefore,
mth term = a0+(m-1)d
= q+p-1-(m-1)
=q+p-1-m+1
=q+p-m
(Proved)
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by @Strange