Question

s the following sequence arithmetic or geometric? Please explain why. -64, -66, -68, ...., ,-100

Answer 1

,-100 Answer:- This is an arithmetic progression. Reason: An arithmetic progression is a sequence of numbers such that the difference between any two successive terms is a constant value. Now, lets look at the sequence of numbers given in the question! We have, -64,-66,-68, ........, Here, the common difference between any two successive terms is – 2 i.e. -66-(-64)=-66+64 = -2 -68 -(-66) = -68 +66 = -2 And so on! Hence clearly the given sequence numbers is in arithmetic progression. In geometric progression we have a sequence of numbers in which any of the term in the sequence after the first term is ob- tained by multiplying the preceding term by a non-zero constant called the common ratio. Clearly, the given sequence of numbers in the question does not fit into the definition of geometric progression. Hence, the given sequence of numbers is in arithmetic progression and not in geometric progression!