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

Solution:

The n-th term of an arithmetic sequence is given by a_n = a + (n - 1)d.

We have to find the 35th term of the arithmetic sequence.

Given, a₁ = -7, a₁₈ = 95

a + (18 - 1)d = 95

a + 17d = 95

We know a = -7

-7 + 17d = 95

17d = 95 + 7

17d = 102

d = 102/17

d = 6

Now, find a₃₅

a₃₅ = a + (35 - 1)d

a₃₅ = -7 + (35 - 1) × 6

a₃₅ = -7 + 34 × 6

a₃₅ = -7 + 204

a₃₅ = 197

Therefore the value of a₃₅ = 197.

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

Summary:

The 35th term of the arithmetic sequence where a₁ = -7 and a₁₈ = 95 is 197.