Answer:
The sum of first 10 terms of the sequence defined by [tex]a_n=3n-3[/tex] is 135.
Step-by-step explanation:
Given : nth term of a sequence as [tex]a_n=3n-3[/tex]
We have to find the sum of first 10 terms of the sequence.
Consider the nth term of a sequence as [tex]a_n=3n-3[/tex]
Then put n = 1 to get the first term
[tex]a_1=3(1)-3=0[/tex]
put n = 2 to get the next term
[tex]a_2=3(2)-3=6-3=3[/tex]
put n = 3 to get the next term
[tex]a_3=3(3)-3=9-3=6[/tex]
put n = 4 to get the next term
[tex]a_4=3(4)-3=12-3=9[/tex]
Thus, the sequence is of the form 0, 3, 6, 9,.....
Thus, the above is an arithmetic sequence with a = 0 and common difference (d) = 3
Thus, Sum of 10 terms is given by
[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]
n = 10 , a = 0 , d = 3
Put we get,
[tex]S_{10}=\frac{10}{2}(2(0)+(10-1)3)[/tex]
Simplify, we have,
[tex]S_{10}=5(9\times 3)[/tex]
[tex]S_{10}=135[/tex]
Thus, the sum of first 10 terms of the sequence defined by [tex]a_n=3n-3[/tex] is 135.
