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The 51st common term of the two arithmetic sequences 15, 19, 23 ...... and 14, 19, 24 ......, is ......
(Important - Enter only the numerical value in the answer)
Correct answer is '1019'. Can you explain this answer?
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The 51st common term of the two arithmetic sequences 15, 19, 23 .........
Arithmetic Sequences
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference. In this question, we have two arithmetic sequences:
Sequence 1: 15, 19, 23, ...
Sequence 2: 14, 19, 24, ...
We are required to find the 51st common term of these two sequences.
Finding the Common Difference
To find the common difference of each sequence, we can subtract any two consecutive terms.
For Sequence 1:
Common Difference = 19 - 15 = 4
For Sequence 2:
Common Difference = 19 - 14 = 5
Finding the 51st Term
To find the 51st term of each sequence, we can use the formula:
Term = First Term + (n - 1) * Common Difference
For Sequence 1:
First Term = 15
Common Difference = 4
n = 51
Term = 15 + (51 - 1) * 4
= 15 + 50 * 4
= 15 + 200
= 215
For Sequence 2:
First Term = 14
Common Difference = 5
n = 51
Term = 14 + (51 - 1) * 5
= 14 + 50 * 5
= 14 + 250
= 264
Finding the Common Term
Now, we need to find the common term between the 51st term of Sequence 1 and the 51st term of Sequence 2.
To do this, we can equate the two terms:
215 = 264
Simplifying this equation, we can see that there is no solution. Therefore, there is no common term between the two sequences.
As a result, the answer to the question is 0.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference. In this question, we have two arithmetic sequences:
Sequence 1: 15, 19, 23, ...
Sequence 2: 14, 19, 24, ...
We are required to find the 51st common term of these two sequences.
Finding the Common Difference
To find the common difference of each sequence, we can subtract any two consecutive terms.
For Sequence 1:
Common Difference = 19 - 15 = 4
For Sequence 2:
Common Difference = 19 - 14 = 5
Finding the 51st Term
To find the 51st term of each sequence, we can use the formula:
Term = First Term + (n - 1) * Common Difference
For Sequence 1:
First Term = 15
Common Difference = 4
n = 51
Term = 15 + (51 - 1) * 4
= 15 + 50 * 4
= 15 + 200
= 215
For Sequence 2:
First Term = 14
Common Difference = 5
n = 51
Term = 14 + (51 - 1) * 5
= 14 + 50 * 5
= 14 + 250
= 264
Finding the Common Term
Now, we need to find the common term between the 51st term of Sequence 1 and the 51st term of Sequence 2.
To do this, we can equate the two terms:
215 = 264
Simplifying this equation, we can see that there is no solution. Therefore, there is no common term between the two sequences.
As a result, the answer to the question is 0.
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The 51st common term of the two arithmetic sequences 15, 19, 23 .........
1019
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The 51st common term of the two arithmetic sequences 15, 19, 23 ...... and 14, 19, 24 ......, is ......(Important - Enter only the numerical value in the answer)Correct answer is '1019'. Can you explain this answer?
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