1. What is the twenty-fifth term of the arithmetic sequence with a1 = –1 and d = –10?
Substitute a1=-1, d=-10, and n=25 in
an = a1 + (n-1)d
Answer: -241
2.What is the twenty-ninth term of arithmetic sequence with a1 = 13 and d = –5/2?
Substitute a1=13, d=-5/2, and n=29 in
an = a1 + (n-1)d
Answer: -57
3. What are the two arithmetic means between –13 and 8?
a1 - -13, a2 = ?, a3 = ?, a4 = 8
Each term differs from the preceding term by d.
a2 is a1 + d, and a3 is a4 - d, so
a1 = -13, a2 = -13+d, a3 = 8-d, a4 = 8
a2 + d = a3
-13+d+d = 8-d
-13+2d = 8-d
3d = 21
d = 7
a2 = -13+7 = -6
a3 = 8-7 = 1
-13, -6, 1, 8
They are -6 and 1
4. What is Sn for the arithmetic series with d = –4, an = 27, and n = 9?
First substitute an = 27, d=-4, and n=9 in
an = a1 + (n-1)d
and solve for a1.
Get a1 = 59
Substitute a1 = 59, d = -4, leave n as just n in
Sn = (n/2)[a1 + (n-1)d]
Simplify
Get
Sn = n(61-2n)
Edwin
