SOLUTION: write the following using sigma notation and find the sum 11,4,-3,-10,....,-143

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Question 1201458: write the following using sigma notation and find the sum 11,4,-3,-10,....,-143
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sum%28%28a%5B1%5D%2B%28n-1%29d%29%2Cn=1%2C%22%3F%22%29

matrix%281%2C2%2Cfirst%2Cterm%29%22%22=%22%22a%5B1%5D%22%22=%22%2211

matrix%281%2C2%2Ccommon%2Cdifference%29%22%22=%22%22d%22%22=%22%224-11=-3-4=-10-%28-3%29=-10%2B3=-7

sum%28%2811%2B%28n-1%29d%29%2Cn=1%2C%22%3F%22%29%22%22=%22%22sum%28%2811%2B%28n-1%29%28-7%29%29%2Cn=1%2C%22%3F%22%29%22%22=%22%22sum%28%2811-7%28n-1%29%29%2Cn=1%2C%22%3F%22%29%22%22=%22%22sum%28%2811-7n%2B7%29%2Cn=1%2C%22%3F%22%29%22%22=%22%22sum%28%2818-7n%29%2Cn=1%2C%22%3F%22%29

we need to find what n equals when 18-7n = -143
                                     -7n = -161
                                       n = 23

sum%28%2818-7n%29%2Cn=1%2C23%29  <-- summation notation for sum

%22%22=%22%22

sum%2818%2Cn=1%2C23%29%22%22-%22%227sum%28%28n%29%2Cn=1%2C23%29%22%22=%22%22

We use the formula for sum%28%28n%29%2Cn=1%2CN%29%22%22=%22%22%28N%28N%2B1%29%29%2F2

18%2A23%22%22-%22%227%2A%28%2823%2823%2B1%29%29%2F2%29%22%22=%22%22414-7%28%2823%2A24%29%2F2%29%22%22=%22%22414-1932%22%22=%22%22-1518  <--sum

Edwin