Letter and Symbol Series Questions and Answers

Answer: A

Correct answer: P

The gaps themselves grow by one each time: A to B is +1, B to D is +2, D to G is +3, G to K is +4. The next gap must be +5, and five beyond K(11) is position 16, which is P. Series of this kind are recognised by the differences rather than by the terms, so writing the gaps underneath is the first move. Assuming a constant gap of four would give O and is the commonest mistake.

Answer: B

Correct answer: Q

The differences increase by one at every step: B to C is +1, C to E is +2, E to H is +3, H to L is +4, so the next must be +5. Five beyond L(12) is position 17, giving Q. Note that the terms are at positions 2, 3, 5, 8, 12, 17 - each is the previous plus the running count. P at 16 would follow from repeating the +4 step instead of increasing it. The running total of the gaps is 1, 3, 6, 10, 15 - the triangular numbers - so the position of the nth term is always the starting position plus a triangular number.

Answer: C

Correct answer: K

The series moves backwards by a growing amount: Z to Y is -1, Y to W is -2, W to T is -3, T to P is -4. The next step is -5, and five below P(16) is position 11, which is K. Growing gaps in reverse are the hardest of these to read, because the letters accelerate away from the end of the alphabet; converting to positions removes the difficulty entirely.

Answer: D

Correct answer: Y

The positions are 1, 4, 9, 16 - the perfect squares. The next square is 25, and position 25 is Y. Reading this as a letter series with growing gaps also works, since the differences are 3, 5, 7 and then 9, but recognising the squares is quicker and leaves no room for a miscount. Z at 26 is the natural guess for anyone who assumes the series ends at the alphabet's close. Squares grow quickly, so a series of this shape gives at most five terms before it passes Z, and recognising that limit is often enough to identify the rule.

Answer: A

Correct answer: R

The gaps widen by one each time: C to D is +1, D to F is +2, F to I is +3, I to M is +4. The next gap is +5, so from M(13) the series reaches position 18, which is R. The pattern is the same as several others of this family but started from a different letter, so the answer cannot be recalled - it has to be counted. Q at 17 results from repeating the previous gap rather than extending it.

Answer: B

Correct answer: X

The steps backwards grow by one: M to L is -1, L to J is -2, J to G is -3, G to C is -4. The next step is -5, and five below C(3) is position -2, which wraps round to X at position 24. Wrapping is what makes this one hard: the series runs off the front of the alphabet and continues from the back. B at 2 is what a single further step would give and is the answer most often chosen. Whenever a series with growing backward steps starts below the middle of the alphabet, a wrap is almost certain, and it is worth checking for one before rejecting the pattern.

Answer: C

Correct answer: R

Two series are interleaved. The terms in the odd positions run A, B, C, advancing by one; those in the even positions run P, Q and so must continue with R. Splitting the series into alternate terms is the standard first move whenever the letters jump about without an obvious single rule. D would be right if the question had asked for the next term of the first series rather than the next term overall.

Answer: D

Correct answer: U

The odd-position terms are B, D, F, climbing two at a time; the even-position terms are Y, W, and so fall two at a time. The next term belongs to the descending series, and two below W(23) is position 21, which is U. Two series moving in opposite directions is a common construction and is invisible until the terms are separated. V at 22 would be a single backward step. A quick test for two interleaved strands is to look at whether the terms alternate between two separate regions of the alphabet, as B, D, F and Y, W, U plainly do here.

Answer: A

Correct answer: C

Separating alternate terms gives M, N, O in the odd positions and A, B in the even ones, each advancing by one. The next term is the third of the second series, which is C. Interleaved series are recognised by the terms alternating between two widely separated parts of the alphabet. P is the tempting answer because it continues the series the eye follows most readily, but it belongs to the wrong strand. The two strands here start far apart, at M and at A, which is what makes the alternation visible at a glance rather than needing the terms to be separated first.

Answer: B

Correct answer: C

One strand runs Z, Y, X, moving backwards from the end of the alphabet; the other runs A, B, moving forwards from the start. The next term belongs to the forward strand and is C. The two strands are converging towards the middle, which is the signature of this construction. W continues the backward strand and is the answer if the alternation is missed. Series in which one strand climbs from A while another falls from Z will meet in the middle, so they cannot run for more than thirteen terms.