Are my answers correct?
8. The first, second, and the nth terms of an arithmetic sequence are 2, 6, and 58 respectively,
i. Find the value of n
n = 15
ii. For that value of n, find the exact value of the sum of n terms.
S_15 = 450
and this :
9. The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetic sequence is 12. Find the first term a1, and the common difference, d, of the sequence.
answer: d = -8, a = 15
Your both answers are completely correct.
i got 3.998
To check if your answers are correct, let's solve the problem step by step.
i. Finding the value of n:
In an arithmetic sequence, the difference between any two consecutive terms remains constant. To find the value of n, we need to find the common difference first.
Common difference (d) = second term - first term = 6 - 2 = 4
Now, let's use the formula for the nth term of an arithmetic sequence to find the value of n:
nth term = first term + (n - 1) * common difference
58 = 2 + (n - 1) * 4
56 = (n - 1) * 4
Dividing both sides by 4:
14 = n - 1
Adding 1 to both sides:
n = 15
So, the value of n is 15.
ii. Finding the exact value of the sum of n terms:
The formula for the sum of an arithmetic sequence is:
S_n = n/2 * (first term + last term)
Substituting the given values:
S_15 = 15/2 * (2 + 58)
S_15 = 15/2 * 60
S_15 = 450
So, according to my calculations, your answers are correct.