#### Question

Between 1 and 31, *m* numbers have been inserted in such a way that the resulting sequence is an A.P. and the ratio of 7^{th} and (*m* – 1)^{th} numbers is 5:9. Find the value of *m*.

#### Solution

Let A_{1}, A_{2}, … A_{m} be *m* numbers such that 1, A_{1}, A_{2}, … A_{m}, 31 is an A.P.

Here, *a* = 1, *b* = 31, *n* = *m* + 2

∴ 31 = 1 + (*m* + 2 – 1) (*d*)

⇒ 30 = (*m* + 1) *d*

Is there an error in this question or solution?

Solution Between 1 and 31, M Numbers Have Been Inserted in Such a Way that the Resulting Sequence is an A.P. and the Ratio of 7th and (M – 1)Th Numbers is 5:9. Find the Value of M. Concept: Arithmetic Progression (A.P.).