Final answer:
To find the missing term in the series 10, 20, 120, 2880, ?, the pattern involves multiplying each term by an increasing factor. The missing term is 2880 multiplied by 120, which equals 345600, making option (a) the correct answer.
Step-by-step explanation:
The student is asking to find the missing term in a mathematical series: 10, 20, 120, 2880, ?. To determine the pattern, we observe how each term relates to its predecessor. Starting with 10 and moving to 20, there is a multiplication by 2. From 20 to 120, the factor moves to 6. Progressing from 120 to 2880, the multiplication factor is 24. Noticing a pattern, each factor is the previous factor multiplied by 3 (2 x 3 = 6, 6 x 4 = 24). If this pattern continues, the next factor would be 24 x 5 = 120. To find the missing term, we need to multiply the fourth term, 2880, by 120. So, the missing term is 2880 x 120 = 345600.
This result corresponds to option (a) 345600, which is the correct option in the final answer.