Given the nth term for each sequence below, how to find the sum of the first 20 terms? (1) #a_n=4n+1# (2) #a_n=n+1/2#

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Answer 1 · 2018-06-29T12:12:52

(1) 860 (2) 220

In both examples we will apply linearity over the sum and use:

#sum_(i=1)^n i = (n(n+1))/2# and #sum_(i=1)^n 1 = n#

(1) #a_n= 4n+1#

To find the sum of the first 20 terms:

#sum_(i=1)^20 (4i+1) = 4sum_(i=1)^20 i+ sum_(i=1)^20 1#

#= 4{{20(20+1))/2} + 20#

#= 4xx210 +20 = 860#

(2) #a_n= n+1/2#

To find the sum of the first 20 terms:

#sum_(i=1)^20 (i+1/2) = sum_(i=1)^20 i+ 1/2sum_(i=1)^20 1#

#= (20(20+1))/2 + 1/2xx20#

#= 210 + 10 = 220#