Question

question 4 of 10
which of the following is most likely the next step in the series?
10a, 21b, 32c, 43d, 54e, 65f
a. 66g
b. 76g
c. 66g
d. 76g
e. 7fg
f. 765

Explanation:

Step1: Analyze the number part

Looking at the numbers: 10, 21, 32, 43, 54, 65. The difference between consecutive numbers is \(21 - 10 = 11\), \(32 - 21 = 11\), etc. So the next number should be \(65+ 11=76\).

Step2: Analyze the letter part

The letters are A, b, C, d, E, f. The pattern is alternating uppercase and lowercase, and the sequence is A (1st letter), b (2nd), C (3rd), d (4th), E (5th), f (6th). So the next letter should be the 7th letter, which is G (uppercase as the pattern alternates: uppercase, lowercase, uppercase, lowercase... and the 7th letter is G, which should be uppercase as the 1st, 3rd, 5th letters are uppercase).

Step3: Analyze the case of the letter

The case pattern: uppercase (A), lowercase (b), uppercase (C), lowercase (d), uppercase (E), lowercase (f). So the 7th term (next term) should be uppercase (since 1st, 3rd, 5th are uppercase; 2nd, 4th, 6th are lowercase; 7th is odd - numbered position, so uppercase). And the letter is G (7th letter of the alphabet). The number is 76. So the next term is 76G? Wait, no, wait the letter case: Wait, A (1, upper), b (2, lower), C (3, upper), d (4, lower), E (5, upper), f (6, lower). So 7th term: number is 65 + 11=76? Wait no, 10,21,32,43,54,65: 10 + 11 =21, 21+11=32, 32+11=43, 43+11=54, 54+11=65, 65+11=76. Correct. Letter: position 1: A (upper), position 2: b (lower), position 3: C (upper), position 4: d (lower), position 5: E (upper), position 6: f (lower), position 7: G (upper). So the term should be 76G? Wait but let's check the options. Wait option B is 76G, option D is 76g. Wait the letter case: the 7th term: the positions: 1 (A, upper), 2 (b, lower), 3 (C, upper), 4 (d, lower), 5 (E, upper), 6 (f, lower), so 7 (G, upper). So the number is 76, letter is G (upper). So the term is 76G? Wait no, wait the previous term is 65f (6th term, lower case). So 7th term: number 65 + 11 =76, letter: f is 6th letter, next is 7th letter G, and case: since 6th is lower, 7th should be upper. So 76G? But wait let's re - check the number sequence: 10,21,32,43,54,65. 10: 1*10 + 0? Wait 10: 1*9+1=10, 21: 2*9 + 3=21? No, 10,21: 10 + 11=21, 21+11=32, yes, common difference 11. So 65 + 11=76. Letter: A(1), b(2), C(3), d(4), E(5), f(6), G(7). Case: upper, lower, upper, lower, upper, lower, so upper. So the term is 76G? Wait option B is 76G, option D is 76g. Wait maybe I made a mistake in case. Wait A (upper), b (lower), C (upper), d (lower), E (upper), f (lower). So the pattern is: for odd - numbered terms (1st, 3rd, 5th), letter is uppercase; for even - numbered terms (2nd, 4th, 6th), letter is lowercase. The next term is the 7th term (odd - numbered), so letter should be uppercase. So 76G. But wait let's check the options again. Option B is 76G, option D is 76g. Wait maybe the number part: 10,21,32,43,54,65. 10: 1 and 0, 21:2 and 1, 32:3 and 2, 43:4 and 3, 54:5 and 4, 65:6 and 5. So the tens digit is 1,2,3,4,5,6, so next tens digit is 7. The units digit is 0,1,2,3,4,5, so next units digit is 6. So number is 76. Letter: A(1), b(2), C(3), d(4), E(5), f(6), G(7). Case: upper, lower, upper, lower, upper, lower, so upper. So the term is 76G. But wait option B is 76G, option D is 76g. Wait maybe the case pattern is different. Wait A (upper), b (lower), C (upper), d (lower), E (upper), f (lower). So the 7th term: odd position, so upper. So 76G. But let's check the options. Option B is 76G, option D is 76g. Wait maybe I messed up the number. Wait 10,21,32,43,54,65. 10 to 21: +11, 21 to 32: +11, 32 to 43: +11, 43 to 54: +11, 54 to 65: +11, 65 to 76: +11. Correct. Letter: A(1), b(2), C(3), d(4), E(5), f(6), G(7). Case: upper, lower, upper, lower, upper, lower, so upper. So the term is 76G. So option B. Wait but let's check again. Wait the original sequence: 10A (10, A, upper), 21b (21, b, lower), 32C (32, C, upper), 43d (43, d, lower), 54E (54, E, upper), 65f (65, f, lower). So the 7th term: number 65 + 11 =76, letter 7th letter (G), case upper (since 7 is odd, same as 1,3,5). So 76G. So option B.

Answer:

B. 76G