The integers P,Q,R and S shown on the number line below are all equally spaced. If R and S are equal to $7^{12}$ and $7^{13}$ , respectively, what is the value of P?

7¹⁰

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7¹¹

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-7¹³

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none of these

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Solution

The correct option is D none of these
The distance between R and S is $7^{13} - 7^{12} = 6 \times 7^{12}$

The distance between two consecutive points is constant.

Value of $Q = 7^{12} - 6 \times 7^{12} = - 5 \times 7^{12}$

Value of $P = - 5 \times 7^{12} - 6 \times 7^{12} = - 11 \times 7^{12}$

The correct answer is option (d).

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