Question

The sum of the first 6 terms of an arithmetic sequence is 3. The sum of the first 12 terms of the same arithmetic sequence is -102. Write the formula for
he general term up of the arithmetic sequence.​

Answer 1

Explaination :—

Sum of the First n Terms of an Arithmetic Sequence :—

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 .

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•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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•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