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The fourth term of a geometric progression is the square of its second term ans the first term is -3. Find it's seventh term.
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Answered by
1
Fourth term of THE G. P. = ar^3
Second term = ar
First term = a = - 3
According to the question,
ar^3 = ( ar) ^2
r^3 / r^2 = a^2 / a
a = r = - 3
So,first term is equal to the common ratio.
Seventh term, a7 = ar^6
a7 = ( - 3) ( - 3 ) ^6
a7 = -3 × 729
a7 = - 2187
Second term = ar
First term = a = - 3
According to the question,
ar^3 = ( ar) ^2
r^3 / r^2 = a^2 / a
a = r = - 3
So,first term is equal to the common ratio.
Seventh term, a7 = ar^6
a7 = ( - 3) ( - 3 ) ^6
a7 = -3 × 729
a7 = - 2187
Anonymous:
Why is 2nd term ar??
a2 = ar^( n-1 ), n= 2 here, so = ar^( 2-1 ) = ar^1 = ar
Also, the series in GP. = a, ar, ar^2, ar^3..... so, 2nd term is ar.
Yup I got it!!
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Answered by
3
Given:
T4=(T2)2
T1=−3 a=−3
ar3=(ar1)2
⇒ar3=a2r2
⇒ar3−a2r2=0
⇒−3r3−9r2=0
⇒3r2(−r−3)=0
⇒r=0or−r−3=0
⇒r=0or=−3
r=−3
Therefore, T7=ar6=(−3)(−3)6=(−3)7=−2187
T4=(T2)2
T1=−3 a=−3
ar3=(ar1)2
⇒ar3=a2r2
⇒ar3−a2r2=0
⇒−3r3−9r2=0
⇒3r2(−r−3)=0
⇒r=0or−r−3=0
⇒r=0or=−3
r=−3
Therefore, T7=ar6=(−3)(−3)6=(−3)7=−2187
Sista this answer is wrong!
ok i m so sorry for that ....just did a little mistake....now i have editted
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hii
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