The fourth term of G.P is greater than first term, which is positive by 372. The third term is greater than the second by 60. Calculate the common ratio and first term of the progression.
Answers
Step-by-step explanation:
Let a be the first term and r be the common ratio of the G.P
a
1
=a, a
2
=ar, a
3
=ar
2
, a
4
=ar
3
By the given condition,
a
3
=a
1
+9
⇒ar
2
=a+9....(1)
a
2
=a
4
+18
⇒ar=ar
3
+18....(2)
From (1) and (2), we get
a(r
2
−1)=9....(3)
ar(1−r
2
)=18....(4)
Dividing (4) and (3), we get
a(r
2
−1)
ar(1−r
2
)
=
9
18
⇒−r=2
⇒r=−2
Substituting the value of r in (1), we get
4a=a+9
⇒3a=9
∴a=3
⇒a
1
=3
⇒a
2
=3(−2)=−6
⇒a
3
=3(−2)
2
=12
⇒a
4
=3(−2)
3
=−24
Thus the first four numbers of the G.P are 3,-6,12 and -24.
Answer:
Let a be the first term and r be the common ratio of the G.P
a1=a, a2=ar, a3=ar2, a4=ar3
By the given condition,
a3=a1+9
⇒ar2=a+9....(1)
a2=a4+18
⇒ar=ar3+18....(2)
From (1) and (2), we get
a(r2−1)=9....(3)
ar(1−r2)=18....(4)
Dividing (4) and (3), we get
a(r2−1)ar(1−r2)=918
⇒−r=2
⇒r=−2
Substituting the value of r in (1), we get
4a=a+9
⇒3a=9
∴a=3
⇒a1=3
⇒a2=3(−2)=−6
⇒a