Question

If the third term of a G.P. is 2, then the product of first five terms is

Answer 1

Let the first term of G.P. be a and common ratio be r, Then,

$T_1 = a \\ \\ T_2 = ar \\ \\ T_3 = ar^{2} \\ \\ T_4 = ar^{3} \\ \\ T_5 = ar^{4} \\ \\ Given, \\ \\ T_2 = ar^{2} = 2 \\ \\ \text{Product of terms} = T_1 * T_2 * T_3 *T_4 * T_5 \\ \\ = a * ar*ar^{2}*ar^{3}*ar^{4} \\ \\ = a^{5} r^{10} \\ \\ = (ar^{2} )^{5} \\ \\ = 2^{5} \\ \\ = 32 \ \ \textbf{Ans.}$

Answer 2

$answer = 32$

Step-by-step explanation:

$given \\ third \: \: term \: \: of \: \: gp \: = ar {}^{2} = 2 \\ product \: \: of \: \: first \: \: five \: \: terms \\ t1 = a \\ t2 = ar \\ t3 = ar {}^{2} \\ t4 = ar {}^{3} \\ t5 = ar {}^{4} \\ a \times ar \times ar {}^{2} \times ar {}^{3} \times ar {}^{4} \\ a {}^{5}r {}^{10} =(ar {}^{2}) {}^{5} \\ (2 ) {}^{5} = 32$