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

Proof

1 Answer
Feb 19, 2016

(see below)

Explanation:

For an arithmetic progression with a difference of dd between terms and an initial value of a_0a0:
color(white)("XXX")a_k=a_0+k*dXXXak=a0+kd

We are told that a_4=a_0+4d=0a4=a0+4d=0

a_11=a_0+11da11=a0+11d
color(white)("XXX")=a_0+4d+7dXXX=a0+4d+7d
color(white)("XXX")=a_4+7dXXX=a4+7d
color(white)("XXX")=7dXXX=7d

a_25=a_0+25da25=a0+25d
color(white)("XXX")=a_0+4d+21dXXX=a0+4d+21d
color(white)("XXX")=a_4+21dXXX=a4+21d
color(white)("XXX")=21dXXX=21d

a_25=3xxa_11a25=3×a11