in an arithmetic series, the first term is -7 and the sum of the first 20 terms is 620 (a) find the common difference. (b) find the value of the 78th term

Answer 1

S_n = (n / 2)[2a₁ + (n -1)d]

620 = (10)(-14 + 19d)

62 = 19d - 14

76 = 19d

4 = d

a₇₄ = -7 + (73)(4)

Answer 2

a1=-7

s20=(n/2)(a1+a20) Gaus's formula

620=(20/2)(a1+a20) n=20, s20=620,

62 =-7 +a20

a20=69

d = (a20-a1)/(n-1) = (69- -7)/(20-1) = 76/19= 4

a78 =a1+d(n-1)=-7+4(77) = 301

a20 = -7+4(19)= 69

common difference =4

78th term is 301

the arithmetic sequence is -7.-3,

1,5,9,13,17,

21,25,29,33,37,

41...

notice the last digit has repeating sequence of 1,5,9,3,7 from the 3rd term on

every 5th term ends in 1 after the 3rd term

the 78th term willl end in an integer of 1: 301.

(78-3)/5 divides evenly = 75/5=17