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Is this correct? Arithmetic sum and sequence #sum_(n=51)^100 7n#

#sum_(n=51)^100 7n#

#S_n=50/2 (357+700)= =26,425#
#a_100=7(51)+7(100−51)=700#

Answer 1

Chloe Alexander

See below.

You need the sum from #n=51# so:

#sum_(n=1)^(100)7n-sum_(n=1)^(50)7n#

#7*(sum_(n=1)^(100)n-sum_(n=1)^(50)n)#

#7*(100/2(2+99)-50/2(2+49))#

#7*(5050-1275)#

#7*(3775)=26425#

#n_100#

First term is 7 and common difference is 7:

#nth# term

#a+(n-1)d#

#n_100=7+(99)*7=700#

So you are correct, or we are both wrong.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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Is this correct? Arithmetic sum and sequence #sum_(n=51)^100 7n#

#sum_(n=51)^100 7n# #S_n=50/2 (357+700)= =26,425# #a_100=7(51)+7(100−51)=700#

#sum_(n=51)^100 7n#

#S_n=50/2 (357+700)= =26,425#
#a_100=7(51)+7(100−51)=700#