Write a recursive formula for the sequence 7, 4, 1, –2, –5, .... Then find the next term. (1 point) an = an–1 – 3, where a1 = –8
2 answers:
Answer: , where
The next term is -8.
Step-by-step explanation:
The given sequence is 7, 4, 1, –2, –5, ................
Here, the first term is
The second term is
The difference =
Similarly,
and so on.
Therefore, the recursive formula for the above sequence will be given by :-
, where d is the common difference.
Since , d=-3
, where
The next term of the sequence is
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k=1
1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.
up to ∞ terms = 2/6
[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+
..∞0] = T²/6
→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+
1/4(3)²+....0] =²/6
[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+
1/(3)²+....x] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6
⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6
⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6
=
↑
[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8
Learn more about the series here brainly.com/question/24295771
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- We know that the sum of any two sides of a triangle is always greater than the third side. So:
- Also the difference of any two sides of a triangle is always less than the third side. Therefore:
Combining the two equations we get:
This means that the third side of the triangle lies between 5cm and 11
Answer: A.