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Find the sum of the first 5 terms of the AP: 10, 6, 2…
- a)–320
- b)512
- c)10
- d)–960
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–...
AP: 10, 6, 2, …
a = 10, d = - 4
Sum of first n terms = S(n) = (n/2) x [2a + (n – 1) x d]
S5 = (5/2) x [2 x (10) + (5 – 1) x (-4)]
= (5/2) x [20 + 4 x (-4)]
= (5/2) x (20 – 16)
= (5/2) x (4)
= 5 x 2
= 10
a = 10, d = - 4
Sum of first n terms = S(n) = (n/2) x [2a + (n – 1) x d]
S5 = (5/2) x [2 x (10) + (5 – 1) x (-4)]
= (5/2) x [20 + 4 x (-4)]
= (5/2) x (20 – 16)
= (5/2) x (4)
= 5 x 2
= 10
Most Upvoted Answer
Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–...
Sum of the first 5 terms of an AP
To find the sum of the first 5 terms of an Arithmetic Progression (AP), you can use the formula:
\[ S_n = \frac{n}{2} \times [2a + (n-1)d] \]
where:
- \(S_n\) is the sum of the first \(n\) terms
- \(n\) is the number of terms
- \(a\) is the first term of the AP
- \(d\) is the common difference between consecutive terms
Given AP
The given AP is: 10, 6, 2, ...
From the given AP, you can identify:
- First term, \(a = 10\)
- Common difference, \(d = 6 - 10 = -4\)
- Number of terms, \(n = 5\)
Calculating the sum
Substitute the values into the formula:
\[ S_5 = \frac{5}{2} \times [2 \times 10 + (5-1) \times (-4)] \]
\[ S_5 = \frac{5}{2} \times [20 + 4 \times (-4)] \]
\[ S_5 = \frac{5}{2} \times [20 - 16] \]
\[ S_5 = \frac{5}{2} \times 4 \]
\[ S_5 = 10 \]
Therefore, the sum of the first 5 terms of the given AP is 10. This matches with option 'C'.
To find the sum of the first 5 terms of an Arithmetic Progression (AP), you can use the formula:
\[ S_n = \frac{n}{2} \times [2a + (n-1)d] \]
where:
- \(S_n\) is the sum of the first \(n\) terms
- \(n\) is the number of terms
- \(a\) is the first term of the AP
- \(d\) is the common difference between consecutive terms
Given AP
The given AP is: 10, 6, 2, ...
From the given AP, you can identify:
- First term, \(a = 10\)
- Common difference, \(d = 6 - 10 = -4\)
- Number of terms, \(n = 5\)
Calculating the sum
Substitute the values into the formula:
\[ S_5 = \frac{5}{2} \times [2 \times 10 + (5-1) \times (-4)] \]
\[ S_5 = \frac{5}{2} \times [20 + 4 \times (-4)] \]
\[ S_5 = \frac{5}{2} \times [20 - 16] \]
\[ S_5 = \frac{5}{2} \times 4 \]
\[ S_5 = 10 \]
Therefore, the sum of the first 5 terms of the given AP is 10. This matches with option 'C'.
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Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer?.
Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the sum of the first 5 terms of the AP: 10, 6, 2…a)–320b)512c)10d)–960Correct answer is option 'C'. Can you explain this answer?.
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