Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Find the first 4 terms of a G.P. if a = -4 and r = -2.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

- 4, 8, - 16, 32, \dots

4, 8, 16, 32, \dots

- 4, - 8, - 16, - 32, \dots

4, 8, - 16, 32, \dots

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

A finite geometric progression or GP sequence in terms of first term a and common ratio r for n terms can be written as a,

{ar}^{2}, {ar}^{3}

{ar}^{4}

,...,

{ar}^{n - 1}

. We see that the given question does not mention the number of terms, so it will be infinite GP as a,

{ar}^{2}, {ar}^{3}

{ar}^{4}

,…..
Mathematically, a sequence with infinite terms is written as
(

\times_{n}

) =

\times_{1} {, \times}_{2},

\times_{3}

,…..
If, a sequence with finite terms is written as
(

\times_{n}

) =

\times_{1} {, \times}_{2},

\times_{3}

,…..

\times_{n}

GP is a type sequence where the ratio between any two consecutive numbers is constant. If (

\times_{n}

) =

\times_{1} {, \times}_{2},

\times_{3}

,….. is an GP, then

\frac{\times_{2}}{\times_{1}}

\frac{\times_{3}}{\times_{1}}

= r………. (i)
Here the ratio between two terms is called the common ratio and denoted as r. The first term is conventionally denoted as a. We put

\times_{1}

= a in equation (1),
r =

\frac{\times_{2}}{\times_{1}} = \frac{\times_{2}}{a}

⇒

\times_{2}

= ar
We can similarly put

\times_{2}

= ar in equation (i),
r =

\frac{\times_{3}}{\times_{2}} = \frac{\times_{2}}{ar}

⇒

\times_{3}

= ar × r = ar2
Similarly, x4 = ar3, x5 = ar4…. We observe that the nth term of GP sequence is arn-1 and we can write the infinite GP sequence in terms of first term a and common ratio r as
a, ar2, ar3, ar4,…..
Given that a = −4 and r = −2
a = −4,
ar2 = (−4)( −2)2 = 8,
ar3 = (−4)( −2)3 = −16,
ar4 = (−4)( −2)4 = 32.
The first 4 terms of a G.P. if a = -4 and r = -2 are

- 4, 8, - 16, 32, \dots

.
Hence the correct answer is option 1.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th