Question

1) if the sum of the cubes of first n natural numbers 25502500, then find the value of n.


2) how many terms are there in the sequence 3,21,147,...........,50421?

Answer 1

Answer:

1)n=100,   2)5 terms

Step-by-step explanation:

1)We know, 1^3+2^3...+n^3=(n(n+1)/2)^2

so, 25502500=(n(n+1)/2)^2

or, 5050=(n(n+1)/2)

or,10100=n(n+1)

or, n^2+n-10100=0

or, n^2+101n-100n-10100=0

therefore, n=100 or -101

Since no. of terms aren't -ve,

n=100

2) 3,21,147... are in G.P.

we know, Tn=a*r^n

or, here,50421=3*7^n

or, 7^n=16807

or, 7^5=7^n

comparing equal bases, we get,

n=5