Question

If fourth term of an A. P. is zero, show that its 25th term is thrice its 11th term.? ( A.P. = arithmetic progression )

Proof

Answer 1

(see below)

Explanation:

For an arithmetic progression with a difference of `d` between terms and an initial value of `a_0`:
`color(white)("XXX")a_k=a_0+k*d`

We are told that `a_4=a_0+4d=0`

`a_11=a_0+11d`
`color(white)("XXX")=a_0+4d+7d`
`color(white)("XXX")=a_4+7d`
`color(white)("XXX")=7d`

`a_25=a_0+25d`
`color(white)("XXX")=a_0+4d+21d`
`color(white)("XXX")=a_4+21d`
`color(white)("XXX")=21d`

`a_25=3xxa_11`