Page 161 - Maths Class 06

Now let us observe triangular patterns made by dots.

1 3 6 10 15
1 + 2 1 + 2 + 3 1 + 2 + 3 + 4 1 + 2 + 3 + 4 + 5

n n( + 1 )
A careful observation gives us the general formula for the terms as , where n represents the nth
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triangular pattern.
EXAMPLE 2. For each pattern of numbers, find 56th term:
(a) 9, 16, 23, 30, 37, ......
(b) 6, 11, 16, 21, 26, 31, 36, ......

SOLUTION : (a) From the sequence, we generalize the formula 7n + 2, where n represents nth term.
\ 56th term = 7 × 56 + 2 = 392 + 2 = 394
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(b) From, the sequence, we generalize the formula 5n + , where n stands for nth term.
\ 56th term = 5 × 56 + 1 = 280 + 1 = 281

Exercise11.1

1. Observe the following dot pattern and:

(a) write down the pattern using numbers.
(b) write down the rule applied to go from one shape to the next.
(c) generalize the statement for the number of dots the nth shape will contain.

2. Look at the pattern of shapes made with matchsticks.

1 2 3 4
How many matchsticks will require to make:
(a) 6th such shape? (b) 21st such shape? (c) nth such shape?

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