Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Solved Examples on Geometric Progression Illustration 1: An infinite G.P. has its first term as x and sum as 5. Then what is the range of x? (2004) Solution: Solution: we know that the sum of an infinite G.P. is S∞ = a/ (1-r), if |r| < 1 = ∞, if |r| ≥ 1 Hence, S∞ = x/(1-r) = 5 Or 1-r = x/5 Hence, r = (5-x)/5 exists only when |r| < 1 Hence, -1 < (5-x)/5 <1 -10 < -x < 0 So this gives 0 < x < 10. Illustration 2: The third term of a geometric progression is 4. What is the product of the first five terms? Solution: here it is given that t3 = 4. Hence, this means ar2 =4 Now product of first five terms = a.ar.ar2.ar3.ar4 = a5r10 = (ar2)5 = 45 Illustration: Consider an infinite geometric series with first term ‘a’ and common ratio ‘r’. Find the values of ‘a’ and ‘r’ if its second term is ¾ and its sum is 4. Solution: It is given in the question that the second term is ¾ and the sum is 4. Further, the first term is ‘a’ and the common ratio is ‘r’. Hence, we have a/ (1-r) = 4 and ar = 3/4. This gives the value of r as 3/4a. So, 4a2/(4a-3) = 4 This gives (a-1)(a-3) = 0 Hence, a = 1 or 3. When a = 1 then r =3/4 and when a = 3 then r = 1/4.
Illustration 1: An infinite G.P. has its first term as x and sum as 5. Then what is the range of x? (2004)
Solution: Solution: we know that the sum of an infinite G.P. is
S∞ = a/ (1-r), if |r| < 1
= ∞, if |r| ≥ 1
Hence, S∞ = x/(1-r) = 5
Or 1-r = x/5
Hence, r = (5-x)/5 exists only when |r| < 1
Hence, -1 < (5-x)/5 <1
-10 < -x < 0
So this gives 0 < x < 10.
Illustration 2: The third term of a geometric progression is 4. What is the product of the first five terms?
Solution: here it is given that t3 = 4.
Hence, this means ar2 =4
Now product of first five terms =
a.ar.ar2.ar3.ar4
= a5r10
= (ar2)5
= 45
Illustration: Consider an infinite geometric series with first term ‘a’ and common ratio ‘r’. Find the values of ‘a’ and ‘r’ if its second term is ¾ and its sum is 4.
Solution: It is given in the question that the second term is ¾ and the sum is 4.
Further, the first term is ‘a’ and the common ratio is ‘r’.
Hence, we have a/ (1-r) = 4 and ar = 3/4.
This gives the value of r as 3/4a.
So, 4a2/(4a-3) = 4
This gives (a-1)(a-3) = 0
Hence, a = 1 or 3.
When a = 1 then r =3/4 and when a = 3 then r = 1/4.
Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.
