The ratio of 7th to the 3rd term of an APis 12:5. Find the ratio of 13

1.	The ratio of 7th to the 3rd term of an APis 12:5. Find the ratio of 13th to the 4th term.ORind five numbers in Arithmetic progression whose sum is 25 and the sum of whose squares4x4 16
Answer» Formula of n th term in AP = a+(n-1)d Where, a is the first term n is the term number d is the common ratio Now when n = 7So, a+(7-1)d=a+6d When n = 3 So, a+(3-1)d=a+2d Since we are given that the ratio of 7th to 3rd term of an AP is 12:5 ⇒(a + 6d)/(a + 2d) = 12/5⇒5a+30d=12a+24d⇒6d = 7a⇒a=6d/7 Now 13th term =a+(13-1)d =a+12d = 4th term =a+(4-1)d =a+3d = Now ratio of 13th and 4th term= (a+ 12d)/(a + 3d)= (6d/7 + 12d) / (6d/7 + 3d)= (90d/7) / (27d/7)= 90/27= 10/3 Thus the ratio of the 13th and 4th term is 10:3

The ratio of 7th to the 3rd term of an APis 12:5. Find the ratio of 13th to the 4th term.ORind five numbers in Arithmetic progression whose sum is 25 and the sum of whose squares4x4 16

Answer»

Formula of n th term in AP = a+(n-1)d

Where, a is the first term n is the term number d is the common ratio

Now when n = 7So, a+(7-1)d=a+6d

When n = 3 So, a+(3-1)d=a+2d

Since we are given that the ratio of 7th to 3rd term of an AP is 12:5 ⇒(a + 6d)/(a + 2d) = 12/5⇒5a+30d=12a+24d⇒6d = 7a⇒a=6d/7

Now 13th term =a+(13-1)d =a+12d =

4th term =a+(4-1)d =a+3d =

Now ratio of 13th and 4th term= (a+ 12d)/(a + 3d)= (6d/7 + 12d) / (6d/7 + 3d)= (90d/7) / (27d/7)= 90/27= 10/3

Thus the ratio of the 13th and 4th term is 10:3