Question

There are n arithmetic means between 3 and 45 such that the sum of arithmetic means is 552

Answer 1

• 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

Answer 2

Given; There are n arithmetic means between 3 and 45 such that the sum of arithmetic means is 552

To Find; The value of n

Solution; There are n arithmetic means between 3 and 45 such that the sum of arithmetic means is 552

a1=3 an=45 Sn=552

an=45

a+(n-1)d=45

3+(n-1)d=45

(n-1)d=42

Sn=552

n(6+(n-1)d)/2=552

n(6+42)/2=552

n*24=552

n=23

Hence the value of n is 23