ntShow that 10,11,12 can'nt be terms of a G.p ?n

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The (m + n)th and the (m - n)th terms of a GP are p and q respectively. Show that the mth and the nth terms of the GP are $\sqrt{p q}$ and ${(\frac{q}{p})}^{(\frac{m}{2 n})}$

Q. Show that the numbers

10, 11, 12

cannot be the terms of a single

G . P .

with common ratio not equal to

1

Q. The p+q term of a GP is m and its p-q term is n show that its p term=√mn.

Q. If

P_{n}

is the sum of a

G P

upto

n

terms. Show that

(1 - r) \frac{d p_{n}}{d r} = n . P_{n - 1} - (n - 1) P_{n}

Q. Let

S

be the sum,

P

be the product and

R

is the sum of reciprocals of

n

terms in a GP.

Prove that

P^{2} R^{n} = S^{n}

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