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1, 3, 5, 7, 1, 3, 5, 7,... The sequence above with the first term, 1,
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Updated on: 20 Oct 2022, 10:12
Updated on: 20 Oct 2022, 10:12
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1, 3, 5, 7, 1, 3, 5, 7,... The sequence above with the first term, 1, repeats in the pattern 1, 3, 5, 7, indefinitely. What is the sum of the values from the 10th term through the 50th term?
(A) 120
(B) 163
(C) 180
(D) 200
(E) 212
(A) 120
(B) 163
(C) 180
(D) 200
(E) 212
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Re: 1, 3, 5, 7, 1, 3, 5, 7,... The sequence above with the first term, 1,
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25 Feb 2022, 22:51
25 Feb 2022, 22:51
1
Carcass wrote:
1, 3, 5, 7, 1, 3, 5, 7,... The sequence above with the first term, 1, repeats in the pattern 1, 3, 5, 7, indefinitely. What is the sum of the values from the 10th term through the 50th term?
(A) 120
(B) 160
(C) 180
(D) 200
(E) 212
(A) 120
(B) 160
(C) 180
(D) 200
(E) 212
We see a repeating pattern of 4
let us find out the 10th and 50th term first
10th term will be \(\frac{10}{4}\), remainder 2 i.e. 3
50th term will be \(\frac{50}{4}\), remainder 2 i.e. 3
We can change the pattern as 3, 5, 7, 1
How many terms do we have?
Inclusive terms = Last - First + 1 = 50 - 10 + 1 = 41
Now, make a set of 4;
(3, 5, 7, 1), (3, 5, 7, 1), (3, 5, 7, 1), ....... , (3, 5, 7, 1) - 10 times and one more term that will be 3
Sum = (3 + 5 + 7 + 1)(10) + 3 = 160 + 3 = 163
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Re: 1, 3, 5, 7, 1, 3, 5, 7,... The sequence above with the first term, 1,
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20 Oct 2022, 08:38
20 Oct 2022, 08:38
1
Given that a sequence is repeated with same 4 terms 1, 3, 5, 7, 1, 3, 5, 7 and we need to find the sum of the values from the 10th term through the 50th term
Term 1 = Term 5 = Term 9
=> If we take remainder of the term number by 4 then the remainder term number and original term number will be same
Ex. Remainder of 5 by 4 is 1 => Term 5 = Term 1
( Watch this video to learn about the Basics of Remainders )
=> Remainder of 10 by 4 is 2 => Term 10 = Term 2 = 3
Similarly, Remainder of 50 by 4 is 2 => Term 50 = Term 2 = 3
So, terms from \(10^{th}\) term to \(50^{th}\) term are 3 , 5, 7, 1, 3, ....., 1, 3
This cycle of 3, 5, 7, 1 will repeat \(\frac{50 - 10}{4}\) = 10 times and then we will have a 3 as the \(50^{th}\) term
=> Sum = 10 * ( 3 + 5 + 7 + 1 ) + 3 = 10 * 16 + 3 = 163
So, Answer will be 163
Hope it helps!
Watch the following video to learn How to Sequence problems
Term 1 = Term 5 = Term 9
=> If we take remainder of the term number by 4 then the remainder term number and original term number will be same
Ex. Remainder of 5 by 4 is 1 => Term 5 = Term 1
( Watch this video to learn about the Basics of Remainders )
=> Remainder of 10 by 4 is 2 => Term 10 = Term 2 = 3
Similarly, Remainder of 50 by 4 is 2 => Term 50 = Term 2 = 3
So, terms from \(10^{th}\) term to \(50^{th}\) term are 3 , 5, 7, 1, 3, ....., 1, 3
This cycle of 3, 5, 7, 1 will repeat \(\frac{50 - 10}{4}\) = 10 times and then we will have a 3 as the \(50^{th}\) term
=> Sum = 10 * ( 3 + 5 + 7 + 1 ) + 3 = 10 * 16 + 3 = 163
So, Answer will be 163
Hope it helps!
Watch the following video to learn How to Sequence problems
