CA Foundation Exam > CA Foundation Questions > The last term of the series 5, 7, 9,….....
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The last term of the series 5, 7, 9,….. to 21 terms is
- a)44
- b)43
- c)45
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The last term of the series 5, 7, 9,….. to 21 terms isa)44b)43c)...
It is a series of odd number without first two entries 1 and 3
general term for odd is (2n - 1) where n >= 1
Series goes like this for odd
(2n - 1), (2n-1+2), (2n-1+2+2),………
(2n-1), (2n+1),(2n+3),…..
But
1 and 3 is not in series so (2n-1) (2n+1) is not taken
So next is (2n + 3)
then general patter here is (2n + 3) where n >= 1
n = 1 then 2X1 + 3 = 5
n = 2 then 2X2 + 3 = 7
For
n = 21
Ans = 2 X 21 +3
= 45
Most Upvoted Answer
The last term of the series 5, 7, 9,….. to 21 terms isa)44b)43c)...
Given series: 5, 7, 9, ..., to 21 terms.
To find: The last term of the series.
Approach:
- We can observe that the series is an arithmetic progression (AP) with a common difference of 2.
- The nth term of an AP is given by the formula: a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
Using the above formula, we can find the last term of the given series as follows:
- First term, a = 5
- Common difference, d = 2
- Number of terms, n = 21 (given)
Substituting the values in the formula, we get:
- Last term, Tn = a + (n-1)d
- T21 = 5 + (21-1)2 = 5 + 40 = 45
Therefore, the last term of the given series is 45.
Hence, the correct option is (c) 45.
To find: The last term of the series.
Approach:
- We can observe that the series is an arithmetic progression (AP) with a common difference of 2.
- The nth term of an AP is given by the formula: a + (n-1)d, where 'a' is the first term and 'd' is the common difference.
Using the above formula, we can find the last term of the given series as follows:
- First term, a = 5
- Common difference, d = 2
- Number of terms, n = 21 (given)
Substituting the values in the formula, we get:
- Last term, Tn = a + (n-1)d
- T21 = 5 + (21-1)2 = 5 + 40 = 45
Therefore, the last term of the given series is 45.
Hence, the correct option is (c) 45.
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The last term of the series 5, 7, 9,….. to 21 terms isa)44b)43c)...
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The last term of the series 5, 7, 9,….. to 21 terms isa)44b)43c)45d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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