Question

The third term in an arithmetic sequence is 58 and the fifth term is 90. If the first term is a1, which is an equation for the nth term of this sequence? A) an=8n +10 B)an=8n-14 C)an=16n+10 D)an=16n-

38

Answer 1

Find d first (d is the common difference).
58, _____, 90
a3 a4 a5
subtract 90-58 = 32
Subtract a5 - a3 = 2
32/2 = 16; d = 16
58 + 16 = 74, 74 + 16 = 90
Next find a1.
an = a1 + (n-1)(d)
Use the a3 that we know and the d.
58 = a1 + (3-1)(16)
58 = a1 + 2(16)
58 = a1 + 32
Subtract 32 from both sides
26 = a1
an = 26 + (n-1)(16)
an = 26 + 16n - 16
an = 16n + 10
Letter C