Question

Calculate the sum of an arithmetic sequence 1,4,7… in first 75 terms​

Answer 1

Answer:

Suppose a sequence of numbers is arithmetic (that is, it increases or decreases by a constant amount each term), and you want to find the sum of the first n terms.

Denote this partial sum by Sn . Then

Sn=n(a1 + an)2 ,

where n is the number of terms, a1 is the first term and an is the last term.

The sum of the first n terms of an arithmetic sequence is called an arithmetic series .

Example 1:

Find the sum of the first 20 terms of the arithmetic series if a1=5 and a20=62 .

S20=20(5 + 62)2S20=670

Example 2:

Find the sum of the first 40 terms of the arithmetic sequence 2,5,8,11,⋯ .

First find the 40th term:

a40=a1+(n−1)d        =2+39(3)=119

Then find the sum:

Sn=n(a1 + an)2S40=40(2 + 119)2=2420

Example 3:

Find the sum:

∑k=150(3k+2)

First find a1 and a50 :

a1=3(1)+2=5a50=3(50)+2=152

Then find the sum:

Sk=k(a1 + ak)2S50=50(5 + 152)2=3925