# If the 4th and 7th terms of a G.P. are 54 and 1458 respectively, find the G.P.

a4 = 54 and a7 = 1458

an = a1rn-1 (n = no. of term, a1 = first term of G.P, r = common ratio)

a4 = a1r3

54 = a1r3 ………(1)

Also, a7 = a1r6

1458 = a1r6 ………(2)

Dividing equation (1) & (2), we get-

r3 = 27

r3 = 33

r = 3

Now, putting value of r in equation (1), we get-

54 = a133

a1 = 2

Now, G.P will be-

a1 , a1r ,a1r2, a1r3,………

2, 2 × 3, 2 × 32, 2 × 3…

2, 6, 18, 54,… is the G.P.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division Lemma49 mins
Fundamental Theorem of Arithmetic- 143 mins
Quiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Relation Between LCM , HCF and Numbers46 mins
Application of Euclids Division Lemma50 mins
Quiz | Fun with Fundamental Theorem of Arithmetic51 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses