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
Alan P.
Feb 19, 2016

(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#

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