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as the nth term of a GP is p. Then Prove thatthe multiplication of the fourt Con-1) number |
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Answer» Let a and r be the first term and common ratio of G.P. respectively. Given, nth term of G.P. = P ∴ ar^n–1 = P ...(1) Product of first 2n –1 terms= a1*a2*a3............*a2n-1= ar*ar^2*ar^3*.......*ar^2n-2= (a*a*a.... *a)*r^[1+2+3....2n-2]= a^2n-1 * r^(2n-2)/2(1 + 2n - 2)= a^2n-1* r^(n-1)(2n-1)= (ar^n-1)^2n-1= P^2n-1 |
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