find the the greatest term of the sequence, 1, 5/2, 25/4 less than 5000
Answers
step by step explaintion please give gormula
Given :- find the the greatest term of the sequence, 1, 5/2, 25/4 less than 5000 ?
Solution :-
As we can see given sequence is in GP with ,
- First term = a = 1 .
- common ratio = r = (5/2).
we know that,
- nth term of GP = Tn = ar^(n-1) .
we have to find greatest term of the sequence less than 5000 .
So,
→ Tn < 5000.
→ a * r^(n - 1) < 5000 .
putting values ,
→ 1 * (5/2)^(n - 1) < 5000.
→ (5/2)^(n - 1) < 5000.
By hit and trial now, putting value of n as 10 and 11, we get,
→ (5/2)^(10 - 1) < 5000.
→ (5/2)^9 < 5000
→ (1953125/512) < 5000.
→ 3814.69 < 5000.
and,
→ (5/2)^(11 - 1) < 5000.
→ (5/2)^10 < 5000 .
→ (9765625/1024) < 5000.
→ 9536.74 > 5000.
Therefore, we can conclude that, the greatest term of the sequence less than 5000 is 10th term.
→ 10 th term of sequence = (5/2)^(10 - 1) = (5/2)^9 = (1953125/512) = 3814.69 . (Ans.)
Learn more :-
Gopi gave 30% of the money he had to his parents,
one-third of the money now left was spent for his p
deposited in the b...
https://brainly.in/question/26795559