Can someone help me with these two questions?
What is the 50th term of the sequence that begins -4, 2, 8, 14...?
What is the 20th term of the sequence that begins -3, 6, -12, 24...?
a = -4
d = 6
T50 = a+49d = -4+49(6) = 290
a = -3
r = -2
T20 = 3(-2)^19 = -1572864
thx steve you were right (thumbs up)
Thank you sooooooo much!!!!!!!!
Of course! I'd be happy to help you with those questions.
To find the 50th term of the sequence that begins with -4, 2, 8, 14..., we need to figure out the pattern in the sequence first. By looking at the numbers, we can see that each term is obtained by adding 6 to the previous term. So, we have a common difference of 6.
To find the nth term of an arithmetic sequence, we can use the formula:
an = a₁ + (n - 1)d,
where:
an represents the nth term of the sequence,
a₁ represents the first term of the sequence,
n represents the position of the term, and
d represents the common difference.
In this case, a₁ is -4, n is 50, and d is 6. Plugging these values into the formula, we can calculate the 50th term as follows:
a₅₀ = -4 + (50 - 1) * 6
= -4 + 49 * 6
= -4 + 294
= 290.
Therefore, the 50th term of the sequence is 290.
Now let's move on to the second question.
To find the 20th term of the sequence that begins with -3, 6, -12, 24..., we need to determine the pattern. Looking at the numbers, we can observe that each term is obtained by multiplying the previous term by -2. So, we have a common ratio of -2.
To find the nth term of a geometric sequence, we can use the formula:
an = a₁ * r^(n - 1),
where:
an represents the nth term of the sequence,
a₁ represents the first term of the sequence,
n represents the position of the term, and
r represents the common ratio.
In this case, a₁ is -3, n is 20, and r is -2. Substituting these values into the formula, we can calculate the 20th term as follows:
a₂₀ = -3 * (-2)^(20 - 1)
= -3 * (-2)^19
= -3 * (-524,288)
= 1,572,864.
Therefore, the 20th term of the sequence is 1,572,864.
I hope this explanation helps! Let me know if there's anything else I can assist you with.