How do you find the arithmetic means of the sequence 3, __, __, __, __, __, 27?

1 Answer
Feb 26, 2017

Answer:

#"The Reqd. Means are, "7,11,15,19 and 23.#

Explanation:

Let the reqd. #5# Arithmetic Means be #A_1,A_2,A_3,A_4,A_5.#

Then, #3,A_1,A_2,A_3,A_4,A_5,27# are #7# terms of an A.P., for

which, in the Usual Notation, #a=3 and a_7=27.#

But, for an A.P., #a_n=a+(n-1)d, n in NN.#

#:. a=3, a_7=27 rArr 27=3+(7-1)d rArr 24=6d rArr d=4.#

Hence, #A_1=a_2=a+d=3=4=7, A_2=a_3=a_2+4=11,#

#A_3=A_2+4=15, A_4=19, A_5=23.#

Thus, the Reqd. Means are, #7,11,15,19 and 23.#

Enjoy Maths.!