'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below.
Observe the given figure carefully. There are 4 dots in first square, 8 dots in second square, 12 dots in third square and so on.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding stimulus
Model Answer
(i)
The number of dots: 4, 8, 12, …
Differences: 8 − 4 = 4, 12 − 8 = 4 (constant)
Since the common difference is constant, the dots form an A.P.
First term (a) = 4, Common difference (d) = 4
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(ii)
$a_n = a + (n-1)d = 4 + (n-1) \times 4 = 4n$
$$\boxed{a_n = 4n}$$
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(iii)
Given: $S_n = 220$
$$S_n = \frac{n}{2}[2a + (n-1)d]$$
$$220 = \frac{n}{2}[8 + 4(n-1)]$$
$$440 = n[4n + 4] = 4n(n+1)$$
$$n(n+1) = 110$$
$$n^2 + n - 110 = 0$$
$$(n-10)(n+11) = 0$$
$$n = 10 \quad (\text{rejecting } n = -11)$$
∴ 10 squares are formed.
Source: Arithmetic Progressions, CBSE Class 10 Mathematics
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Explanation
- (i) Just show the differences are equal — that's enough for 1 mark. State a and d clearly.
- (ii) Substitute the formula directly; simplify to 4n. Examiners expect the simplified form.
- (iii) Use the sum formula (not nth term). Set up the quadratic, solve, and reject the negative root — both steps carry marks. Always state why n = −11 is rejected.