1,-1/2,1/4..
are in GP.. then find 8th term.
Answers
Answered by
2
Answer:
r=2
a
8
=a
1
(2)
8−1
192=a
1
(2)
7
192=a
1
(2)
7
2
7
192
=a
1
2
7
192
×2
12−1
=a
12
2
7
192
×2
11
=a
12
a
12
=192×2
4
a
12
=3072
Answered by
270
Question :-
1,-1/2,1/4 are in GP . then find 8th term. ?
Solution :-
→ First Term of GP = a = 1
→ Common Ratio = Second Term / First Term = (-1/2) / 1 = (-1/2)
we have to find 8th term of this GP.
we know that, The nth term of a GP series is Tn = a*r^(n-1), where a is first term and r is common ratio.
So,
→ a = 1
→ r = (-1/2)
→ n = 8
Putting all values we get :-
→Tn = a*r^(n-1)
→ T(8) = 1 * (-1/2)^(8 - 1)
→ T(8) = (-1/2)^7
→ T(8) = (-1)^7 / (2)^7
→ T(8) = (-1) / 128
→ T(8) = (-1/128) (Ans.)
Hence, 8th term of the GP is (-1/128) .
___________________
Extra :-
→ sum of n terms of GP = a[(1 - r^n) / (1 - r)]
→ sum of infinite terms of GP = a/(1 - r)
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