Please help describe the sequence as arithmetic geometric or neither. For arithmetic and geometric sequences give the common difference or common ratio.
1. {3,-6,12,-24,-48...}
2.{-11/4,-2,-5/4,-1/2,1/4...}
3.{3600,1440,576,230.4,...}
4.{600,-300,100,-25...}
#1. check for common difference
-6-3 = -9; 12-(-6) = 18 ≠ -9 so not arithmetic
check for common ratio
-6/3 = -2; 12/-6 = -2 so the common ratio is -2; geometric
(assuming the ratio holds for the rest of the terms)
Now you try the others.
1. The given sequence {3, -6, 12, -24, -48...} is neither an arithmetic nor a geometric sequence. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. However, in this sequence, the terms do not follow a consistent pattern of either adding or multiplying by a constant.
2. The given sequence {-11/4, -2, -5/4, -1/2, 1/4...} is an arithmetic sequence. The common difference can be determined by subtracting each term from its subsequent term. In this case, the common difference is 3/4.
3. The given sequence {3600, 1440, 576, 230.4...} is a geometric sequence. The common ratio can be determined by dividing each term by its subsequent term. In this case, the common ratio is 1/4.
4. The given sequence {600, -300, 100, -25...} is neither an arithmetic nor a geometric sequence. Like the first sequence, the terms do not follow a consistent pattern of either adding or multiplying by a constant.
To determine whether a given sequence is arithmetic, geometric, or neither, we need to examine the pattern between consecutive terms.
1. {3, -6, 12, -24, -48, ...}
This sequence is neither arithmetic nor geometric because there is no consistent pattern between consecutive terms. The terms alternate between positive and negative values, but the differences between terms do not follow a constant common difference or ratio.
2. {-11/4, -2, -5/4, -1/2, 1/4, ...}
This sequence is arithmetic because there is a consistent pattern between consecutive terms. The common difference can be found by subtracting any term from its previous term. Here, the common difference is 3/4, as each term is obtained by adding 3/4 to the previous term.
3. {3600, 1440, 576, 230.4, ...}
This sequence is geometric because there is a consistent pattern between consecutive terms. The common ratio can be found by dividing any term by its previous term. Here, the common ratio is 0.4, as each term is obtained by multiplying the previous term by 0.4.
4. {600, -300, 100, -25, ...}
This sequence is neither arithmetic nor geometric because there is no consistent pattern between consecutive terms. The terms alternate between positive and negative values, but the differences between terms do not follow a constant common difference or ratio.