Question

A vendor arranged his apples as in the following pattern:
(a) If there are ten rows of apples, can you find the total number of apples without actually counting?
(b) If there are twenty rows, how many apples will be there in all?
Can you recognize a pattern for the total number of apples? Fill the chard and try!

Rows	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Total apples	$1$	$3$	$6$	$10$	$15$

Answer 1

As we can see that in 1st row,there is $1$ apple. in 2nd row,there are $2$ apples.in 3rd row, $3$ apples and so on .

So total number of apples in the n row will be $n(n+1)/2$

(a) total number of apples in $10$ rows = $(10\times 11)/2=55apples$

(b) total number of apples in $20$ rows = $(20\times 21)/2=210apples$.

Rows	1	2	3	4	5	6	7	8	9
Total apples	1	3	6	10	15	21	28	36	45

The pattern is $n(n+1)/2$ where n is the number of rows.