00:01
In the given question, the following statement is given to us and we are told to determine whether the statement is true or false.
00:08
So it says that the sum which is denoted as sn of the first n terms of an arithmetic sequence given as an, whose first term is a1 is found using the formula.
00:22
Sn equals n by 2 times a1 plus an.
00:26
So what we could do now is we already know the sum or sum to n terms or let's write it like this.
00:35
Sum of first n terms, sum of first n terms of an arithmetic sequence of an arithmetic sequence is given by the formula.
00:53
It is denoted as s and it is denoted by the formula n by 2 times 2a plus n minus 1 times d so this is the general formula that we use to find the sum of first n terms of an arithmetic sequence right but over here in the statement the formula that is given is different right so we what we could do first is let's just rearrange this formula that we have, right? so we can write s n as equal to n by two times a plus a instead of 2a we can write it as a plus a plus n minus 1 times d.
01:43
And now you can see that we also know another formula in arithmetic sequence, which is the nth term of an arithmetic sequence which is denoted as a n, a, n, is found by the formula a plus n minus 1 times d...