SOLUTION: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7

Algebra ->  Sequences-and-series -> SOLUTION: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7      Log On


   

Question 1178154: Consider each given sequence start. i) Classify each as arithmetic, geometric, and/or none of these. ii) Find the 28th term. iii) Find the sum of the first 7 terms, call it S7 .
88,83, 78, 73,
Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

88,83, 78, 73,
common difference between consecutive terms is -5
first term a = 88
tn = a + (n-1)*d
t28 = 88+(87)*-5
t28 = -347
Sum of terms = Sn = n/2(2a+(n-1)d)
S7 = (7/2)(2*88+ 6*-5)
S7 =(7/2) * 146
S7 =511

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

88,83, 78, 73,...
1st term a%5B1%5D=88
2nd term a%5B2%5D=83=88-5
3rd term a%5B3%5D=78=83-5
=> common difference is d=-5

i) Classify each as arithmetic, geometric, and/or none of these.
=> common difference is d=5, so you have an arithmetic sequence
nth term formula will be:
a%5Bn%5D=a%5B1%5D-d%28n-1%29
a%5Bn%5D=88-5%28n-1%29


ii) Find the 28th term.
a%5B28%5D=88-5%2828-1%29
a%5B28%5D=88-5%2827%29
a%5B28%5D=88-135
a%5B28%5D=-47

iii) Find the sum of the first 7+terms, call it S7 .
first find 5th, 6th, and 7th term
a%5B5%5D=88-5%285-1%29=88-5%2A4=88-20=68
a%5B6%5D=88-5%286-1%29=88-5%2A5=88-25=63
a%5B7%5D=88-5%287-1%29=88-5%2A56=88-30=58

88,83, 78, 73,68,63,58

the sum is S%5B7%5D=88%2B83%2B78%2B73%2B68%2B63%2B58=511