Question
If (a−b)2,(a2+b2) are the first two terms of an AP, then which of the following will be the next term?
Answer: Option B
:
B
Given,
a1=(a−b)2
a1=a2+b2−2ab
and
a2=a2+b2
Now,
d=a2−a1
d=a2+b2−a2−b2+2ab
⇒d=2ab
The next term
a3=a2+d
a3=a2+b2+2ab=(a+b)2
∴Nextterm(a3)=(a+b)2
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:
B
Given,
a1=(a−b)2
a1=a2+b2−2ab
and
a2=a2+b2
Now,
d=a2−a1
d=a2+b2−a2−b2+2ab
⇒d=2ab
The next term
a3=a2+d
a3=a2+b2+2ab=(a+b)2
∴Nextterm(a3)=(a+b)2
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