# Consider the following statements: 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each

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Consider the following statements:

1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP.

2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP.

Which of the above statements is/are correct?

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

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Correct Answer - Option 3 : Both 1 and 2

Concept:

Multiplying or dividing with a non-zero number does not change the common ratio of the G.P

Calculation:

Multiplying or dividing with a non-zero number does not change the common ratio of the G.P

Let us consider sequence a1, a2, a3 …. an is a G.P.

Common ratio = r = $\rm a_2\over a_1$ = $\rm a_3\over a_2$ = $\rm a_n\over a_{n-1}$

If each term is multiplied/ divided by the same non-zero number it will be the same r value. So, the sequence will not change.