If a - b - c are in A-P- then 3 a - 3 b - 3 c are in G-P-A- TrueB- False

The correct option is A True Consider the AP a,b,c. Let b=a + d and c= nbsp;a + 2d. i.e., a, a+d, a+2d are in AP. ⇒ The sequence 3^a, 3^b, 3^c nbsp; nbsp ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Implicit Differentiation

If a , b , c ...

Question

If $a, b, c$ are in A.P., then $3^{a}, 3^{b}, 3^{c}$ are in G.P..

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
True

Consider the AP $a, b, c .$
Let $b = a + d$ and $c = a + 2 d .$
i.e., $a, a + d, a + 2 d$ are in AP.

$\Rightarrow$ The sequence $3^{a}, 3^{b}, 3^{c}$ becomes
$3^{a}, 3^{a + d}, 3^{a + 2 d} .$ $\equiv 3^{a}, 3^{a} \times 3^{d}, 3^{a} \times {(3^{d})}^{2},$ a G.P. with common ratio $3^{d}$ and first term $3^{a} .$

Suggest Corrections

Similar questions

Q. If

a, b, c

are in

A . P

, then show that

3^{a}, 3^{b}, 3^{c}

are in

G . P

If a, b, c are in A.P. then $3^{a}$ , $3^{b}$ , $3^{c}$ are in ___.

Q. Assertion :The number of ways in which three distinct numbers can be selected from the set

{3^{1}, 3^{2}, 3^{3}, . . ., 3^{100}, 3^{101}}

so that they form a G.P. is 2500. Reason: If a, b, c are in A.P., then

3^{a}, 3^{b}, 3^{c}

are in G.P.

If a, b, c are in A.P. then $3^{a}$ , $3^{b}$ , $3^{c}$ are in

Q. Four points given by position vectors

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

are coplanar, where

\to a, \to b a n d \to c

are non-coplanar vectors.

Join BYJU'S Learning Program

If a,b,c are in A.P., then 3a,3b,3c are in G.P..

The correct option is A True Consider the AP a,b,c. Let b=a+d and c=a+2d. i.e., a,a+d,a+2d are in AP. ⇒ The sequence 3a,3b,3c becomes 3a,3a+d,3a+2d.≡3a,3a×3d,3a×(3d)2, a G.P. with common ratio 3d and first term 3a.

If $a, b, c$ are in A.P., then $3^{a}, 3^{b}, 3^{c}$ are in G.P..