Question

product of 3 consecutive gp terms is 2744. find out first term

Answer 1

well , your question is incomplete. here we have given only one clue. but there are two unknown terms. so, not possible to find first term as usual . but it's possible to find 2nd terms as you can see below description.

Let three consecutive terms in geometric progression is a/r , a , ar .

product of three consecutive terms = 2744
(a/r)(a)(ar) = 2744

a³ = 14 × 14 × 14 = 14³

taking cube root both sides,

a = 14

hence, 2nd term in gp is 14.

Answer 2

Let 3 consecutive term of gp are a/r,a,ar

Where a is the first term of gp

And r is the common ratio of gp

So ,  given that  

product of these term = 2744

(a/r)×a×(ar) = 2744

a^3 = 2744

So,

a = 14

If there is any confusion please leave a comment below.