The ratio of the 3rd term and the 7th term of an arithmetic province is 5:7 What is the ratio - Maths - Arithemetic Sequences

Question

The ratio of the 3rd term and the 7th term of an arithmetic
province is 5:7 What is the ratio of the 4th to the 8th term?

Manbar Singh · Accepted Answer

Let a be the first term and d be the common difference of the AP
Now, a3a7 = 57 given⇒a + 2da + 6d = 57⇒7a + 14d = 5a +
30d⇒7a - 5a = 30d - 14d⇒2a = 16d⇒a = 8d 1now,
a4a8 = a + 3da + 7d⇒a4a8 = 8d + 3d8d + 7d using 1⇒a4a8
=11d15d = 1115

The ratio of the 3rd term and the 7th term of an arithmetic province is 5:7.What is the ratio of the 4th to the 8th term?