 Hello and welcome to the session. I am Asha and I am going to help you with the following question which says, the sum of n terms of two arithmetic progressions are in the ratio 5n plus 4 is to 9n plus 6 find the ratio of their 18 terms. Let's start with the solution and let a1 d1 be the first term common difference n difference s1 be the sum of n terms n terms of the second a p series. So, s1 will be equal to n upon 2 to a1 plus n minus 1 into d1, s2 will be equal to n upon 2 into 2 into a2 plus n minus 1 into d2. Now, we are given ratio of s1 and s2 is equal to 5n plus 4 upon 9n plus 6. Now, s1 is n upon 2 into 2 a1 plus n minus 1 into d1 upon n minus upon 2 to a2 plus n minus 1 into d2. This is equal to 5n plus 4 upon 9n plus 6 upon 2 cancels out with n upon 2 and further up 2 a1 plus n minus 1 into d1 upon 2 a2 plus n minus 1 into d2 is equal to 5n plus 4 upon 9n plus 6. Let this be equation number one. Now, according to the equation, we have to find the ratio of their 18th term. This we have to find term of first a p is term of second a p. Just now find 18th term of a p upon 8th term of is equal to a1 plus 18 minus 1 into d1 upon a2 plus 18 minus 1 into d2. Since to find the a and a term, we have to formalize a plus n minus 1 into d, where a is the first term of the a p series and d is the common difference. Now, multiplying the numerator and denominator of the right hand side by 2, 18th term of second a p is equal to a1 plus this is 17 d1. So, when multiplying with 2, we have 34 d1 upon 282 plus 34 d2. Look of equation one, which is 2 a1 plus n minus 1 into d1 upon 282 plus n minus 1 into d2, which is equal to 5n plus 4 upon 9n plus 6. We get, for n is equal to 35, we will get the 18th term of first a p upon 18th term of second a p. So, for n is equal to 35, let us find its value. So, this is 2 a1 plus 35 minus 1 into d1 upon 282 plus 35 minus 1 into d2. So, this is equal to 5 into 35 plus 4 upon 9 into 35 plus 6, which further implies that 2 a1 plus 34 d1 upon 282 plus 34 d2 is equal to 179 upon 321 and this is nothing but the 18th term a p upon the 18th term of second a p is equal to 179 upon 321. Therefore, our answer is ratio the 18th term with the progression is equal to 179 upon 321. So, this completes our conversation. Take care and bye for now.