Question

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

Answer 1

`"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.!