# Statement 1:The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000. Statement  2: for any natural number n. Option 1) Statement 1 is false, statement 2 is true Option 2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 Option 3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 Option 4) Statement 1 is true, statement 2 is false

As we learnt in

Sequence -

Arragement of real numbers specified in a definite order, by some assigned law.

- wherein

Notations -

or

Statement 1 :  $1+(1+2+4)+(4+6+9)+....+(361+380+400)\; is\; 8000$

Statement 2 :      $\sum_{k=1}^{n}(k^{3}-(k-1)^{3})=n^{3}$

Statement 1 : $T_{1}=1,T_{2}=7=8-1$

$T_{3}=19=27-8\Rightarrow T_{n}=n^{3}-(n-1)^{3}$

$\therefore \;$  Statement 2 is a correct explanation of statement 1.

Option 1)

Statement 1 is false, statement 2 is true

This option is incorrect.

Option 2)

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

This option is correct.

Option 3)

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

This option is incorrect.

Option 4)

Statement 1 is true, statement 2 is false

This option is incorrect.

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