Question

I NEED help!

1. In an arithmetic sequence, the 8th term is 17 and the 17th term is -10. Show all work for each of the following:

a) Determine the common difference of the sequence.
b) Find the first term of the sequence.
c) Find the 77th term of the sequence.

2. How many multiples of 7 are there between 250 and 340?

Answer 1

the correct anser is -3, 38, -190

Answer 2

a) To determine the common difference of the sequence, subtract the 17th term (-10) from the 8th term (17) to get a common difference of 27.

b) To find the first term, subtract the common difference (27) from the 8th term (17) a total of 7 times to get the first term of -144.

17th term (-10)

- (common difference of 27)

- -144

c) To find the 77th term, take the first term (-144) and add the common difference (27) a total of 76 times to get the 77th term of 1062.

-144

+ (common difference of 27)

+ 1062

2. To find the number of multiples of 7 between 250 and 340, begin by finding the greatest multiple of 7 which is less than 250. This would be the multiple of 7 with the value of 245. Next, Find the least multiple of 7 between 250 and 340. This would be the multiple of 7 with the value of 336. Finally, to get the number of multiples of 7 between 250 and 340, subtract 245 from 336 and then add 1 to get the answer.

336 - 245 + 1 = 92

Explanation: