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?
Both 1 and 2
Concept:
Multiplying or dividing by a non-zero number does not change the common ratio of a G.P.
Calculation:
Multiplying or dividing by a non-zero number does not change the common ratio of a G.P.
Let the sequence a1, a2, a3 …. an be 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, the r value will remain the same. Thus, the sequence will not change.
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