Question

A pattern of letter arrangements begins with the 3 steps below. first continue the pattern for 3 more steps:

1. A
2.ABA
3.ABCBA
4.
5.
6.

how many letters are in each step above?

how many letters do you think there will be in step 10?

Answer 1

1, 3, 5, 7, 9, 11

19

Explanation:

Given,

Step 1 : A,

Step 2 : ABA

Step 3 : ABCBA

By proceeding the pattern,

Remaining steps are,

Step 4 : ABCDCBA,

Step 5 : ABCDEDCBA

Step 6 : ABCDEFFEDCBA

Thus, the number of letters in each steps are,

1, 3, 5, 7, 9, 11

Which is an AP having first term, a = 1,

Common difference, d = 3 - 1 = 2,

Hence, the number of letters in step 10 = 10th term of the above AP

= a + (10-1)d

= 1 + 9(2)

= 1 + 18

= 19

Answer 2

1)
4. ABCDCBA
5. ABCDEDCBA
6. ABCDEFEDCBA

2) 1, 3, 5, 7, 9, 11

3) 19