Question
If the tth term of an AP is s and sth term of the same AP is t, then an is ___.
Answer: Option B
:
B
Given,
at=a+(t−1)d=s,...(i)
as=a+(s−1)d=t...(ii)
⇒(t−s)=a+(s−1)d−a−(t−1)d
⇒t−s=(s−t)d[from eqns. (i) and (ii)]
⇒(t−s)=−(t−s)d
⇒d=−1
From (i), we get
a+(t−1)(−1)=s.
⇒a=s+t−1
an=a+(n−1)d
⇒an=s+t−1+(n−1)×(−1)=s+t−1−n+1=s+t−n
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:
B
Given,
at=a+(t−1)d=s,...(i)
as=a+(s−1)d=t...(ii)
⇒(t−s)=a+(s−1)d−a−(t−1)d
⇒t−s=(s−t)d[from eqns. (i) and (ii)]
⇒(t−s)=−(t−s)d
⇒d=−1
From (i), we get
a+(t−1)(−1)=s.
⇒a=s+t−1
an=a+(n−1)d
⇒an=s+t−1+(n−1)×(−1)=s+t−1−n+1=s+t−n
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