Question

find the sum of first 20th term of arithamatic sequence 8, 15, 22etc​

Answer 1

Answer:

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

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The formula for the sum of terms of an arithmetic series is really very intuitive. You take the arithmetic average of the first and the last member you want to add, and then you multiply it by the number of the members.

s(n)=n∗(a(1)+a(n))/2

So we only have to find the 26-th member of this sequence. We first must find the difference d . You can do this by subtracking any member of the sequence from the following one. We get:

d=a(2)−a(1)=15–8=7

The formula for the n-th member of the sequence is also simple and intuitive. You take the first member and add the difference d (n−1) times.

a(n)=a(1)+(n−1)∗d

Now we can calculate the 26-th member.

a(26)=a(1)+25∗d=8+25∗7=8+175=183

And finally, we can plug this number to our formula for the sum of the members.

s(26)=26∗(8+183)/2=13∗191=2483

Step-by-step explanation:

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