In a certain A.P the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term .

Explanation

Let a and d be thie fridt and common difference of the given A.P
`thereforea_24=a+(24-1)d=a+23d.`
`a_(10)=a+(10-1)d=a+9d`
Given`a_(24)=2a_(10)`
`rArra+23d-2a+18d`
`rArr5d.`
`a_(72)=+(72-1)d=a+71``a_(34)=a+(34-1)d`. Clearly `a_(72)=2a_(34)`.