Question

What is the sum of the first 10 terms of the sequence defined by an=3n-3?

Answer 1

Answer:

The sum of first 10 terms of the sequence defined by $a_n=3n-3$ is 135.

Step-by-step explanation:

Given : nth term of a sequence as $a_n=3n-3$

We have to find the sum of first 10 terms of the sequence.

Consider the nth term of a sequence as $a_n=3n-3$

Then put n = 1  to get the first term

$a_1=3(1)-3=0$

put n = 2 to get the next term

$a_2=3(2)-3=6-3=3$

put n = 3 to get the next term

$a_3=3(3)-3=9-3=6$

put n = 4 to get the next term

$a_4=3(4)-3=12-3=9$

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

$S_n=\frac{n}{2}(2a+(n-1)d)$

n = 10 , a = 0 , d = 3

Put we get,

$S_{10}=\frac{10}{2}(2(0)+(10-1)3)$

Simplify, we have,

$S_{10}=5(9\times 3)$

$S_{10}=135$

Thus, the sum of first 10 terms of the sequence defined by $a_n=3n-3$ is 135.

Answer 2

The answer is D. 135