Question

Write the correct number in the given boxes from the following A. P.
(i) 1, 8, 15, 22,...
Here a = $\boxed{x}$, t₁ = $\boxed{x}$, t₂ = $\boxed{x}$, t₃ = $\boxed{x}$,
t₂ – t₁ = $\boxed{x}$ – $\boxed{x}$ = $\boxed{x}$
t₃ – t₂ = $\boxed{x}$ – $\boxed{x}$ = $\boxed{x}$ ∴ d = $\boxed{x}$

(ii) 3, 6, 9, 12,...
Here t₁ = $\boxed{x}$, t₂ = $\boxed{x}$, t₃ = $\boxed{x}$, t₄ = $\boxed{x}$,
t₂ – t₁ = $\boxed{x}$, t₃ – t₂ = $\boxed{x}$ ∴ d = $\boxed{x}$

(iii) –3, –8, –13, –18,...
Here t₃ = $\boxed{x}$, t₂ = $\boxed{x}$, t₄ = $\boxed{x}$, t₁ = $\boxed{x}$,
t₂ – t₁ = $\boxed{x}$, t₃ – t₂ = $\boxed{x}$ ∴ a = $\boxed{x}$, d = $\boxed{x}$

(iv) 70, 60, 50, 40,...
Here t₁ = $\boxed{x}$, t₂ = $\boxed{x}$, t₃ = $\boxed{x}$,...
∴ a = $\boxed{x}$, d = $\boxed{x}$

Answer 1

(i) 1, 8, 15, 22,...
Here a = $\boxed{1}$, t₁ = $\boxed{1}$, t₂ = $\boxed{8}$, t₃ = $\boxed{15}$,
t₂ – t₁ = $\boxed{8}$ – $\boxed{1}$ = $\boxed{7}$
t₃ – t₂ = $\boxed{15}$ – $\boxed{8}$ = $\boxed{7}$ ∴ d = $\boxed{7}$

(ii) 3, 6, 9, 12,...
Here t₁ = $\boxed{3}$, t₂ = $\boxed{6}$, t₃ = $\boxed{9}$, t₄ = $\boxed{12}$,
t₂ – t₁ = $\boxed{6-3=3x}$, t₃ – t₂ = $\boxed{9-6=3}$ ∴ d = $\boxed{3}$

(iii) –3, –8, –13, –18,...
Here t₃ = $\boxed{-13}$, t₂ = $\boxed{-8x}$, t₄ = $\boxed{-18x}$, t₁ = $\boxed{-3x}$,
t₂ – t₁ = $\boxed{-8-\left(-3\right)=-5x}$, t₃ – t₂ = $\boxed{-13-\left(-8\right)=-5x}$ ∴ a = $\boxed{-3}$, d = $\boxed{-5x}$

(iv) 70, 60, 50, 40,...
Here t₁ = $\boxed{70}$, t₂ = $\boxed{60}$, t₃ = $\boxed{50}$,...
∴ a = $\boxed{70}$, d = $\boxed{-10x}$