Question

If tñ=2ñ+3, find S10​

Answer 1

`S_(10)=280`

Explanation:

Given that,

`t_n=2n+3` ...(1)

We need to find the value of
`S_(10)`.

Put n = 1 to find the first term.

`t_1=2(1)+3=5`

Put n = 2 to find the second term.

`t_2=2(2)+3=7`

Put n = 3 to find the third term.

`t_3=2(3)+3=9`

Put n = 10 to find the tenth term.

`t_(10)=2(10)+3=23`

It means we need to find the sum of 5,7,9,.....,23.

The formula for the sum of n terms is given by :

`S_=(n)/(2)(a+a_n)`

We have, n = 10, a = 5 and
`a_n=23`

So,

`S=(10)/(2)(5+23)\\\\S_(10)=10* 28\\\\=280`

So, the value of
`S_(10)` is equal to 280.