Question

How do I find the indicated value?

Answer 1

nth term = 1st term + (rate)*(n-1)

so the 65th term with a first term of -17 and a rate of 8 would be 495

Answer 2

65ᵗʰ Term of the sequence is 479

50ᵗʰ Term of the sequence is 346

Explanation:

1.)

Here,

First Term = a₁ = 3

Second Term = a₂ = 10

Third Term = a₃ = 17

Now,

Common Difference (d)

d = a₂ - a₁ = (-7) - (-15) = -7 + 15 = 8

d = a₃ - a₂ = 1 - (-7) = 1 + 7 = 8

Here, Common Difference is same everywhere

Now, For 65ᵗʰ term, n = 65

aₙ = a + (n - 1)d

a₆₅ = (-15) + (65 - 1) × 8

a₆₅ = (-15) + 64 × 8

a₆₅ = (-15) + 512

a₆₅ = 479

Thus, 65ᵗʰ Term of the sequence is 479

2.)

Here,

First Term = a₁ = -15

Second Term = a₂ = -7

Third Term = a₃ = 1

Now,

Common Difference (d)

d = a₂ - a₁ = 10 - 3 = 7

d = a₃ - a₂ = 17 - 10 = 7

Here, Common Difference is same everywhere

Now, For 50ᵗʰ term, n = 50

aₙ = a + (n - 1)d

a₅₀ = 3 + (50 - 1) × 7

a₅₀ = 3 + 49 × 7

a₅₀ = 3 + 343

a₅₀ = 346

Thus, 50ᵗʰ Term of the sequence is 346

-TheUnknownScientist