Question

if the 3rd term of a gp is 4, find the product of the first 5 terms

Answer 1

Let a be the first term and r be the common difference.

Given that 3rd term of a gp is 4.

t3 =  4

ar^3 - 1 = 4

ar^2 = 4.  ----- (1).


The product of 1st 5 terms = a * ar^2 * ar^3 * ar^4 * ar^5

                                             = $a^{5} r^{1+2+3+4+5}$

                                             = $a^{5} r^{10}$

                                             = $(a r^{2})^5$

                                            = (4)^5

                                            = 1024.



Hope this helps!

Answer 2

a3=
$a3 = 4 \\ a {r}^{2} = 4 \\ product = {a}^{2} \times {r}^{1 + 2 + 3 + 4} \\ {a}^{5} \times {r}^{10} \\( a {r}^{2} ) ^{5} \\ {4}^{5} \\ 1024$