Evaluate each arithmetic series described

Question

a₁= 28, a_n= 173, n =30

Answer 1

a1 = 28

a30 = 173

a30 = a1 + 29d where d = the common difference

a30 = 173 = 28+29d

29d = 173-28 = 145

d = 145/29 =5 = the common difference = an- a(n-1) = any term minus the preceding term

an = a1 +(n-1)(d) is the general equation for the nth term of an arithmetic sequence

an = 28 +(n-1)(5) = 28+5n-5 = 23+5n

an = 23 +5n is the equation for the nth term of a sequence with a1=23 and d=5

a30 = 23+5(30) = 23+150 = 173

a1= 28

a2 = 33

a3 = 38

a4 = 43

a5 = 48

a6 = 53

a7 = 58

...

a29 = 168

a30 = 173

odd terms end in 8

even terms end in 3