# Ch-13 Letter Series : Introduction & Formula

In some of the questions involving alphabetical series, a set of letters is written four or five times with blank spaces, in between. The series follows a specific pattern and the candidate is required to find out the letters which should come in place of the missing spaces. Pattern on which a series is written, is not well defined and hence can follow any method which an examiner can think of. Thus the alphabetical series may look like any of the following series :

abcde, bcdea, cdeab, deabc, ………….,

Here, in 1^{st} repetition of the sequence abcde, 1^{st} letter is taken to the end of the sequence which then becomes bcdea. Using the rame procedure, the next repetition yields the sequence cdeab and so on.

abcde, abcee, abeee, aeeee, …..,

Here, the successive letters towards the end of the series are replaced bye, the last of the letters of each sequence.

uvw.xy,yuvwx, .xyuvw, ……,

Here, the last letter in the previous set is made 1^{st} letter of the next set and so on.

Following examples will make the students understand the method as how to approach questions based on alphabetical series.

**1. What are the missing letters in the following series? pq r – – rs prs – – spq-**

(a) pqppq (b) spqpr (c) sqpqr (d) sqprq

**Sol.** Here, the block which is repeated, consists of four letters pqrs. Rewriting the series in block of four letters, we get pqrs, – rsp, rs – -, spq – and now filling the blank spaces, we observe that the series must be pqrs, qrsp, rspq, spqr so that the missing letters are sqpqr. Thus, (c) is the correct option.

**2. What are the last five missing-letters in the following series? **

**b – b – cab – baca – cba – a**

(a) cacbbb (b) cacbcb (c) cabcbc (d) caccqc

**Sol.** The longest available chain of letters in the given series is baca. Two other such blocks are formed if we fill up 4th space from left and 3rd space from right, so that the series now looks like

b – bacab – baca – cbaca –

The filled up sequence now suggests that the series will be

bcba ca bcba ca bcba ca b

Therefore, the missing letters are acbcb. Thus, (b) is the right option.

**3. Find the missing letters in the following series:**

uv – u – ww- -xu-vv-

(a) vwxuu (b) vuvuv (c) uvxuv (d) vuxuu

**Sol.** The presence of the term uww and then the letter next to w, which is x, in the ninth position (the blocks are of three letters) suggests the series to be uvv, uww, uxx, uuvv, u.

So the missing letters are vuxuu and, hence (d) is the correct option.

**4. Find the last five missing letters of the series:**

** a – aabb – – ab – b – – — **

(a) baaaa (b) babab (c) baaba (d) bbaaa

Sol. The presence of the terms aabb in the middle suggests the form of the series to be ab, aabb, followed by aaabbb, aaaa. Thus, (a) is the correct option.

**5. Find the missing letters in the following series: **

**adb – ac – da – cddcb – dbc – cbda **

(a) bccba (b) cbbaa (c) ccbba (d) bbcad

**Sol.** In the above series, the letters are equidistant from the beginning and end.

adbcac b da b cddcb a dbc a cbda

Hence, the missing letters are cbbaa. Therefore, the correct option is (b).