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The number of terms in the sequence -17, -10, -3,…., 144 is:
- a)26
- b)25
- c)27
- d)24
Correct answer is option 'D'. Can you explain this answer?
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The number of terms in the sequence -17, -10, -3,…., 144 is:a)26...
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The number of terms in the sequence -17, -10, -3,…., 144 is:a)26...
Counting the number of terms in the sequence:
To find the number of terms in the given sequence, we need to determine the pattern and then calculate the total number of terms.
Finding the pattern:
- The sequence starts at -17 and increases by 7 in each step.
- The next term after -17 is -17 + 7 = -10.
- Continuing in the same manner, we get the terms: -3, 4, 11, 18, ..., 144.
Calculating the total number of terms:
- To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
nth term = a + (n-1)d
where a is the first term, d is the common difference, and n is the number of terms.
- Applying this formula to the last term of the sequence (144), we get:
144 = -17 + (n-1)7
144 = -17 + 7n - 7
161 = 7n - 7
168 = 7n
n = 24
Conclusion:
- The total number of terms in the sequence -17, -10, -3, ..., 144 is 24.
- Therefore, the correct answer is option 'D' (24 terms).
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The number of terms in the sequence -17, -10, -3,…., 144 is:a)26b)25c)27d)24Correct answer is option 'D'. Can you explain this answer?
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