Numerical: number series MCQ - Practice Questions with Answers

Each term decreases by 111. From 975 to 864 the difference is 111, from 864 to 753 again 111, and from 753 to 642 again 111. Continuing the same pattern, 642 minus 111 equals 531. The number 431 would require a drop of 211, so it breaks the pattern. The number 541 is 101 less than 642, not 111. The number 532 is close, but it is 110 less than 642, so it is not the correct continuation.

The pattern can be read as consecutive cubes plus consecutive products: 2^3 + 2 x 3 = 14, 3^3 + 3 x 4 = 39, 4^3 + 4 x 5 = 84, and 5^3 + 5 x 6 = 155. The next term should be 6^3 + 6 x 7 = 216 + 42 = 258, not 260. The numbers 39, 84 and 155 fit the same rule, so they are not the wrong terms in the series.

The sequence follows consecutive cubes with 1 added: 2 cubed plus 1 gives 9, 3 cubed plus 1 gives 28, 4 cubed plus 1 gives 65, and 5 cubed plus 1 gives 126. The next term must therefore be 6 cubed plus 1, which is 216 plus 1, or 217. The numbers 204, 194 and 206 do not fit this cube-plus-one pattern, so they cannot complete the series.

Separate the sequence into odd and even positions. The even-position terms are 4, 8, 12, 16, increasing by 4 each time. The odd-position terms are 1, 3, 7, -, 21; their differences are +2, +4, +6 and +8. Therefore the missing odd-position term is 7 + 6 = 13. The values 19, 14 and 15 do not maintain both patterns, especially the increasing even-step pattern inside the odd-position subsequence.

The terms follow the pattern n cubed plus n squared. For n equal to 1, 1 cubed plus 1 squared gives 2. For 2, 8 plus 4 gives 12; for 3, 27 plus 9 gives 36; for 4, 64 plus 16 gives 80; and for 5, 125 plus 25 gives 150. The next value uses n equal to 6: 216 plus 36 equals 252. The numbers 210, 258, and 270 do not fit this cube-plus-square pattern.