Sequential arrangements of blocks are formed according to a pattern. Each arrangements of blocks are formed according to a pattern. Each arrangement after the first one is generated by adding a row of squares to the bottom of the previous arrangement, as shown in the figure to the right. If this pattern continues, which of the following gives the number of squares in the $n$ th arrangement?

2 n^{2}

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2 (2 n - 1)

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\frac{n (+ 1)}{2}

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n (n + 1)

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n^{2} + 1

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Solution

The correct option is A $\frac{n (+ 1)}{2}$
If similar pattern goes on then nth arrangement have (1+2+........+n) & this sum is equal to n(n+1)/2.

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The correct option is A n(+1)2If similar pattern goes on then nth arrangement have (1+2+........+n) & this sum is equal to n(n+1)/2.

The correct option is A $\frac{n (+ 1)}{2}$
If similar pattern goes on then nth arrangement have (1+2+........+n) & this sum is equal to n(n+1)/2.