Question

the algebric expression of arithmetic sewuence is 2n+3 find the sum of first 10 terms of the arthemetic sequence​

Answer 1

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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 S n . Then

S n = n ( a 1   +   a n ) 2 ,

where n is the number of terms, a 1 is the first term and a n is the last term.

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

Answer 2

Answer:

It is given that

an = 2n - 3

If n = 1, 

a1 = 2(1) - 3 = 2 - 3 = -1

First term is -1.

If n = 2,

a2 = 2(2) - 3 = 4 - 3 = 1

Second term is 1.

If n = 3, 

a3 = 2(3) - 3 = 6 - 3 = 3

Third term is 3.

So the sequence is -1, 1, 3 ….

We observe that the series are in arithmetic progression with a1 = -1 and difference d = 2

The formula for the sum of n terms is

Sn = (n/2)[2a + (n – 1)d]

We know that

n =10, a = -1, and d = 2 

Substituting the values

S10 = (10 / 2) [2(-1) + (10 - 1)(2)]

S10 = 5 [-2 + 18]

S10 = 5 × 16 = 80

Therefore, the sum of the first ten terms is 80.