00:01
Hello students.
00:01
Today we will discuss about this question.
00:04
In this question we are given that the first, the sum of first 15 terms that is equals of the arithmetic series.
00:19
So here ap that is equals to 225 and the sum of next 15 term that is equals to 705.
00:34
So here we need to to find the first term and the common difference d, hence we need to determine the 10th term.
00:45
So t10 also.
00:47
So here we can write, we can write first of all that is let the first term that is equals to a and common difference that is equals to d.
01:09
So here the sum of n terms of ap that can be given as that is equals to sn is equal to n divided by 2 in bracket 2a plus n minus 1 multiplied by d.
01:23
So here the sum of the first 15 term that is 225.
01:29
So as 15 that is equals to 225.
01:32
So if we put n that is equals to 15 then therefore we can write 220.
01:39
That is equals to 15 divided by 2 in bracket 2a plus 15 minus 1 multiplied by d so that is equals to that implies that 2a plus 14 d that is equal to 225 divided by 15 multiplied by 2 so that implies that 2 in bracket a plus 7d that is equals to 15 multiplied by 2 so that implies that a plus 7d that is equals to 15 this will be equation 1 now we are given that the sum of next 15 term that is 705 where the first term that is so the first term that will be that is equals to a plus 15d that is equal to 16 term so therefore that implies that 15 divide by 2 in bracket multiplied by 2a plus 15 d plus 15 minus 1 multiplied by d that is equals to 705 so therefore that implies that we will get 2a plus 30 d plus 14 d that is equals to 705 divided by 15 multiplied by 2 so that is equals to 47 multiplied by 2 so therefore we can write 2 in bracket a plus 22d that is equal to 47 multiplied by 2 so that implies that a plus 22d that is equals to 47 this will be equation 2 now we will subtract equation 1 from equation 2 so that implies that we can write a plus 22d minus a minus 70d that is equals to 47 minus 15 so that implies that 15d that is equal to 32 so that that implies that d that is equals to 32 divided by 15.
03:42
Now the value of d put in equation 1...