Given below are two statements:
Statement I : An arithmetic progression is a sequence in which the sum of any two consecutive terms is a constant.
Statement II : In a geometric progression, the ratio of any term to its preceding term is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Statement I is incorrect but Statement II is correct
An arithmetic progression is defined by a constant difference between consecutive terms; a geometric progression by a constant ratio.
Statement I: An arithmetic progression is a sequence in which the sum of any two consecutive terms is a constant. Incorrect. What stays constant in an AP is the difference of consecutive terms, the common difference \(d\). In 2, 5, 8, 11, … the difference is always 3, but the sums of consecutive terms are 7, 13, 19, …, which keep changing.
Statement II: In a geometric progression, the ratio of any term to its preceding term is a constant. Correct. This constant is the common ratio \(r\). In 3, 6, 12, 24, … each term divided by the one before it gives 2.