Question

Match each arithmetic series with the correct sum.

(a) a1​=76,an​=176,n=21
(b) a1​=58,an​=−7,n=26
(c) 5+11+17+...+95
(d) d=−1/4,n=20,an​=−53/12
(e) d=7,n=18,an​=72

Answer 1

To find the sum of an arithmetic series, use the formula Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term. The sums for the given arithmetic series are: (a) 5292, (b) 663, (c) 800, (d) -85/3, and (e) 648.

Step-by-step explanation:

To find the sum of an arithmetic series, we can use the formula Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term. Let's calculate the sums for each given arithmetic series:

(a) a1 = 76, an = 176, n = 21: Sn = (21/2)(76 + 176) = 21(252) = 5292

(b) a1 = 58, an = -7, n = 26: Sn = (26/2)(58 + (-7)) = 13(51) = 663

(c) 5 + 11 + 17 + ... + 95: First, we need to find the number of terms using the formula an = a1 + (n - 1)d, where d is the common difference. 95 = 5 + (n - 1)(6), n = 16. Then, Sn = (16/2)(5 + 95) = 8(100) = 800

(d) d = -1/4, n = 20, an = -53/12: Sn = (20/2)(-1/4 + (-53/12)) = 10(-17/6) = -85/3

(e) d = 7, n = 18, an = 72: Sn = (18/2)(0 + 72) = 9(72) = 648