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1Exercise 9.1
Find the 12th term of the AP 3, 7, 11, 15, ...
▶ Show Detailed Solution
a = 3, d = 4
a₁₂ = a + 11d = 3 + 11(4) = 3 + 44 = 47
2Exercise 9.1
Find the sum of the first 20 terms of the AP 2, 5, 8, 11, ...
▶ Show Detailed Solution
a = 2, d = 3
S₂₀ = (20/2)[2(2) + (20-1)(3)]
= 10[4 + 57]
= 10 × 61 = 610
3Exercise 9.1
Which term of the GP 2, 6, 18, ... is 1458?
▶ Show Detailed Solution
a = 2, r = 3.
aₙ = 2 × 3n-1 = 1458
3n-1 = 729 = 3⁶
n - 1 = 6 ⇒ n = 7
The 7th term is 1458.
4Exercise 9.1
Find the sum to n terms of the GP 3, -6, 12, -24, ...
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a = 3, r = -2.
Sₙ = a(1 - rⁿ)/(1 - r)
= 3(1 - (-2)ⁿ)/(1 - (-2))
= 3(1 - (-2)ⁿ)/3
= 1 - (-2)ⁿ
5Exercise 9.1
Find the sum to infinity of the GP 1/3, 1/9, 1/27, ...
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a = 1/3, r = 1/3 (|r| < 1).
S∞ = a/(1 - r) = (1/3)/(1 - 1/3) = (1/3)/(2/3) = 1/2
6Exercise 9.1
Find the sum to n terms of the series 1² + 2² + 3² + ... + n².
▶ Show Detailed Solution
Sum of squares: Σn² = n(n+1)(2n+1)/6
This is a standard formula.
For n = 5: S = 5(6)(11)/6 = 55