Question

Assertion: If $a, b, c$ are in A.P., then $b+c, c+a, a+b$ are in A.P.
Reason: If $a , b , c$ are in A.P., then $10^{ a }, 10^{ b }, 10^{ c }$ are in G.P.

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct

Answer 1

Answer: (B)

Assertion: $b + c , c + a , a + b$ will be in A.P.
if $( c +a)-( b + c )=( a + b )-( c + a )$
i.e. if $2b = a + c$ i.e. if $a , b , c$ are in A.P.
Reason: $10^{ a }, 10^{ b }, 10^{ c }$ are in G.P. if $\frac{10^{ b }}{10^{ a }}=\frac{10^{ c }}{10^{ b }}$
i.e. if $10^{b-a}=10^{c-b}$
i.e. if $b - a = c - b$
$ \Rightarrow 2 b = a + c$ which is true.