Question

If is the arithmetic mean between a' and b', then, find the value of n'.

Answer 1

Answer:

n=0

Step-by-step explanation:

Arithmetic mean of a and b is=[a+b]/2

thus

[a+b]/2=[a^n+1+b ^n+1]/a^n+b^n

[a+b]/2=a^n*a+b^n*b/a^n+b^n (ax+y=ax*ay)

Then by cross multiplication we get

a^na+a^nb+b^na+b^nb=2a^na+2b^nb

a^nb+b^na=a^na+b^nb

a^nb-a^na=b^nb-b^na

a^n(b-a)=b^n(b-a)

a^n=b^n

a and b can only be = if n=0 (x^n=1)

thus n=0

Answer 2

• LET a1,a2,.......,an BE n ARITHMETIC MEAN

• a,a1,a2,.......,an,b ARE in A.PNo OF TERMS

• =n+2let d BE THE COMMON DIFFERENCE.

• b=a+(n+2−1)db−a=(n+1)d⇒d=b−an+1