Answer:
-679
Explanation:
We know that the following sequence is in arithmetic progression. To determine the 78th term, we need to use the arithmetic progression formula (aₙ = a₁ + (n - 1)d), where aₙ = nth term, a₁ = first term of the sequence, and d = common distance between two terms in a sequence.
Here, we know that the nth term is 78 as we need to find the 78th term of the sequence. Therefore, we can claim n = 78 to be true.
We also know that the first term of the sequence (14, 5, -4), is 14 as we can observe that the first integer of the sequence (a.k.a, the initial start of the sequence) is 14. Therefore, we can also claim a₁ = 14 to be true.
Lastly, we can observe the common difference (or distance) between two terms in the sequence is -9.
- We can check this by using the formula aₙ₊₁ - aₙ = d.
- aₙ = a₁ = 14, then aₙ₊₁ = a₁₊₁ = a₂ = 5; so: aₙ₊₁ - aₙ = a₂ - a₁ = 5 - 14 = -9 = d
- aₙ = a₂ = 5, then aₙ₊₁ = a₂₊₁ = a₃ = -4; so: aₙ₊₁ - aₙ = a₃ - a₂ = -4 - 5 = -9 = d
Therefore, we can claim d = -9 to be true.
Now we can plug in these variables into the formula:
- aₙ = a₁ + (n - 1)d ⇒ aₙ = (14) + (78 - 1)(-9)
Finally, simplify until you get a simplified numeral (a number that cannot be further simplified using the four mathematical operations).
- ⇒ aₙ = (14) + (78 - 1)(-9)
- ⇒ aₙ = (14) + (77)(-9)
- ⇒ aₙ = (14) + (77)(-9)
- ⇒ 14 - 693 = -679
Therefore, the 78th term of the sequence is -679.