Question

If the third term of a geometric series is 3, find the product of its first five terms.​

Answer 1

Answer:

$\implies answer$

$Third \: term \: of \: GP = ar ^{2} = 3$

$General \: term = ar ^{n - 1}$

$Product \: of \: first \: five \: terms = a ^{5} .r ^{0 + 1 + 2 + 3 + 4}$

$a ^{5} r ^{10} = (ar ^{2} ) ^{5} \\ = (3) ^{5} \\ = 243$

Answer 2

Answer:

⟹answer

Third \: term \: of \: GP = ar ^{2} = 3ThirdtermofGP=ar

2

=3

General \: term = ar ^{n - 1}Generalterm=ar

n−1

Product \: of \: first \: five \: terms = a ^{5} .r ^{0 + 1 + 2 + 3 + 4}Productoffirstfiveterms=a

5

.r

0+1+2+3+4

\begin{gathered}a ^{5} r ^{10} = (ar ^{2} ) ^{5} \\ = (3) ^{5} \\ = 243\end{gathered}

a

5

r

10

=(ar

2

)

5

=(3)

5

=243