the second term of an arithmetic sequence is -16 and the eight term is 8. what is the sum of the first 10 terms?

Answer:So, we know a_2 = -16 and a_8 = 8The formula for an arithmetic sequence is:a_n = a_1 + (n-1)dSo, plugging both will result in two equations:-16 = a_1 + (2 - 1)d8 = a_1 + (8 - 1)d-16 = a_1 + d8 = a_1 + 7dSo, we have a system of linear equations, so just solve by using elimination method, or by simply subtracting like terms.-24 = - 6dd = 4So, the common difference is 4, checking manually by adding 4,-20, -16, -12, -8, -4, 0, 4, 8To get the sum of the first 10 terms, we can use the arithmetic series formulaS_n = n/2 (2a_1 + (n-1)d)we know n = 10 (since sum of the first 10 terms)a_1 = -20d = 4Substituting the ternsS_10 = 10/2 ( 2(-20) + (10-1)4 )= 5 ( -40 + (9)4 )= 5 (-40 + 36 )= 5 ( - 4 )= -20So the sum of the series is -20

Answered by crypticshot | 2025-08-26