If for an exponential function y - ax a - 0 - a1 - x 1-x2 - x3 - xn form an A - P - then y1 - y2 - yn form a

The correct option is D A . P . x_2 x_1 = x_3 x_2 = x_4 x_3 .... = d #160; given #160; y_1y_2 = a^x_1a^x_2 = a^x_ ...

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GCD of Polynomials

If for an exp...

Question

If for an exponential function $y = a^{x} (a > 0), a_{1} \neq x_{1}, x_{2}, x_{3} . . . . . x_{n}$ form an A . P . then $y_{1}, y_{2}, . . . . y_{n}$ form a

A . P .

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G . P .

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H . P

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Solution

The correct option is D A . P .
$x_{2} - x_{1} = x_{3} - x_{2} = x_{4} - x_{3} . . . . = d$ given

$\frac{y_{1}}{y_{2}} = \frac{a^{x_{1}}}{a^{x_{2}}} = a^{x_{1} - x_{2}} = a^{- d}$

$\frac{y_{2}}{y_{3}} = \frac{a^{x_{2}}}{a^{x_{3}}} = a^{x_{2} - x_{3}} = a^{- d}$

$\frac{y_{1}}{y_{2}} = \frac{y_{2}}{y_{3}} = y_{1} y_{3} = y_{2}^{2}$

Therefore $y_{1}, y_{2}, . . . . y_{n}$ forms A.P

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If for an exponential function y=ax(a>0),a1≠x1,x2,x3.....xn form an A . P . then y1,y2,....yn form a

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If for an exponential function $y = a^{x} (a > 0), a_{1} \neq x_{1}, x_{2}, x_{3} . . . . . x_{n}$ form an A . P . then $y_{1}, y_{2}, . . . . y_{n}$ form a