Question

Sum of first 5 term is 125 and first 10 term 400.​

Answer 1

Answer:

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

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Sum of the First n Terms of an Arithmetic Series

If a series is arithmetic the sum of the first n terms, denoted Sn , there are ways to find its sum without actually adding all of the terms.

To find the sum of the first n terms of an arithmetic series use the formula, n terms of an arithmetic sequence use the formula,

Sn=n(a1 + an)2 ,

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

The series 3+6+9+12+⋯+30 can be expressed as sigma notation ∑n=1103n . This expression is read as the sum of 3n as n goes from 1 to 10

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

2,5,8,11,14,⋯

First find the 40 th 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=5a20=3(50)+2=152

Then find the sum:

Sk=k(a1 + ak)2S50=50(5 + 152)2=3925

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