sequence 4,8,12,16,find the common defference 15th terms and the sum of the first 15 terms​

Step-by-step explanation:Finding the Common Difference This sequence is an arithmetic sequence because there's a constant difference between consecutive terms. To find the common difference, subtract any term from the one that follows it: - 8 - 4 = 4- 12 - 8 = 4- 16 - 12 = 4 Therefore, the common difference is 4. Finding the 15th Term The general formula for the nth term of an arithmetic sequence is: - a_n = a_1 + (n-1) * d where: - a_n is the nth term- a_1 is the first term- d is the common difference- n is the number of the term In this case: - a_1 = 4- d = 4- n = 15 So, the 15th term (a_15) is: - a_15 = 4 + (15 - 1) * 4- a_15 = 4 + 14 * 4- a_15 = 4 + 56- a_15 = 60 Therefore, the 15th term is 60. Finding the Sum of the First 15 Terms The formula for the sum of the first n terms of an arithmetic sequence is: - S_n = (n/2) * [2 * a_1 + (n-1) * d] In this case: - n = 15- a_1 = 4- d = 4 So, the sum of the first 15 terms (S_15) is: - S_15 = (15/2) * [2 * 4 + (15 - 1) * 4]- S_15 = 7.5 * [8 + 14 * 4]- S_15 = 7.5 * [8 + 56]- S_15 = 7.5 * 64- S_15 = 480 Therefore, the sum of the first 15 terms is 480.follow more

Answered by policarpionicholaikl | 2024-10-21