Question

In the sequence 1,2,2,3,3,3,4,4,4,4,....... Then what is 150th term

Answer 1

Answer:17

Step-by-step explanation:1,2,2,3,3,3,3,4,4,4,4.......

1 is repeated once. 2 is repeated twice, 3 is repeated thrice and so on.

in the 10th position is 4.

as you can clearly see it forms an AP. 1+2+3+4+10

in the same way, 1+2+3+.......n terms=150

using the formulae Sn=n/2[2a+(n-1)d)

150=n/2[2+n-1]

=>300=n(n+1)

=>n2+n-300=0

Now it has taken the form of a quadratic equation

Solving it, using quadratic formulae, the roots = [-b+(b2-4ac)1/2]/2a

=(-1+​​12011/2)/2

the roots are -17.82 and 16.825.

since the no. of terms i.e. n has to be positive, the ans is 16.825 or 17 (rounding it off to nearest integer).

therefore the 150th term in the original series would be 17.