Answer:
[tex]S_{10}=280[/tex]
Step-by-step explanation:
Given that,
[tex]t_n=2n+3[/tex] ...(1)
We need to find the value of [tex]S_{10}[/tex].
Put n = 1 to find the first term.
[tex]t_1=2(1)+3=5[/tex]
Put n = 2 to find the second term.
[tex]t_2=2(2)+3=7[/tex]
Put n = 3 to find the third term.
[tex]t_3=2(3)+3=9[/tex]
Put n = 10 to find the tenth term.
[tex]t_{10}=2(10)+3=23[/tex]
It means we need to find the sum of 5,7,9,.....,23.
The formula for the sum of n terms is given by :
[tex]S_=\dfrac{n}{2}(a+a_n)[/tex]
We have, n = 10, a = 5 and [tex]a_n=23[/tex]
So,
[tex]S=\dfrac{10}{2}(5+23)\\\\S_{10}=10\times 28\\\\=280[/tex]
So, the value of [tex]S_{10}[/tex] is equal to 280.
