Question

Identify the 35th term of an arithmetic sequence where a1 = −7 and a18 = 95.

Answer 1

Th term of an arithmetic sequence:

We have to find the difference (d)

an=a₁+(n-1)d

Data:
a₁=-7
a₁₈=95

95=-7+(18-1)d
95+7=17d
17d=102
d=102/17
d=6

Now, we can calculate the 35 th term of an arithmetic sequence:
a₃₅=-7+(35-1)*6
a₃₅=-7+34*6
a₃₅=-7+204
a₃₅=197

Answer: the 35th term of this arithmetic sequence is 197. (a₃₅=197)