Question

The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a₁,

which is an equation for the nth term of this sequence?

Answer 1

an = 8n = 14

Step-by-step explanation:

a1 = the first term
d= common difference

a1, (a1 + d), (a1 + 2d), …, a1 + ((n - 1)d),…

the third term is:
10 = a1 + 2d - - (1)

and the fifth term:
26 = a1 + 4d - - (2)

subtract: (2) - (1)

16 = 2d -> d = 8

subtract into (1)
10 = a1 + 2 x 8
-> a1 = - 6

so, the nth term:

an = a + (n - 1)

an = -6 + 8(n-1)

an = 8n — 14

hope this helps!