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Sum of first 5 terms of an A.P. is one fourth of the sum of next five terms. If the first term = 2, then the common difference of the A.P. is
- a)3
- b)6
- c)- 6
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Sum of first 5 terms of an A.P. is one fourth of the sum of next five ...
Given information:
- Sum of first 5 terms of an A.P. is one fourth of the sum of next five terms.
- First term of A.P. is 2.
To find: Common difference of the A.P.
Let's assume the common difference of the A.P. as 'd'. Then, the first five terms of the A.P. will be:
2, 2 + d, 2 + 2d, 2 + 3d, 2 + 4d
Sum of first 5 terms = 2 + (2 + d) + (2 + 2d) + (2 + 3d) + (2 + 4d)
= 10 + 10d
Now, let's find the sum of next five terms. The next five terms will be:
2 + 5d, 2 + 6d, 2 + 7d, 2 + 8d, 2 + 9d
Sum of next 5 terms = (2 + 5d) + (2 + 6d) + (2 + 7d) + (2 + 8d) + (2 + 9d)
= 20 + 35d
Given, Sum of first 5 terms = (1/4) * Sum of next 5 terms
=> 10 + 10d = (1/4) * (20 + 35d)
=> 40 + 40d = 20 + 35d
=> 5d = -20
=> d = -4
Therefore, the common difference of the A.P. is -4. Hence, option (c) is correct.
- Sum of first 5 terms of an A.P. is one fourth of the sum of next five terms.
- First term of A.P. is 2.
To find: Common difference of the A.P.
Let's assume the common difference of the A.P. as 'd'. Then, the first five terms of the A.P. will be:
2, 2 + d, 2 + 2d, 2 + 3d, 2 + 4d
Sum of first 5 terms = 2 + (2 + d) + (2 + 2d) + (2 + 3d) + (2 + 4d)
= 10 + 10d
Now, let's find the sum of next five terms. The next five terms will be:
2 + 5d, 2 + 6d, 2 + 7d, 2 + 8d, 2 + 9d
Sum of next 5 terms = (2 + 5d) + (2 + 6d) + (2 + 7d) + (2 + 8d) + (2 + 9d)
= 20 + 35d
Given, Sum of first 5 terms = (1/4) * Sum of next 5 terms
=> 10 + 10d = (1/4) * (20 + 35d)
=> 40 + 40d = 20 + 35d
=> 5d = -20
=> d = -4
Therefore, the common difference of the A.P. is -4. Hence, option (c) is correct.
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Community Answer
Sum of first 5 terms of an A.P. is one fourth of the sum of next five ...
A1 + a2 + a3 + a4 + a5 = 1/4 ( a6 + A7 + a8 + a9 +a10 ) (1)
Now let,
a2 = ( a1 + d )
a3 = a1 + 2d
a4 = a1 + 3d
a10 = a1 + 9d
Put this in Equation (1)
we get
5a + 10d = 1/4 ( 5a + 35d )
Put a = 2
we get
30-35 = 5d
Therefore d= -6
Hope you have understand this answer
Now let,
a2 = ( a1 + d )
a3 = a1 + 2d
a4 = a1 + 3d
a10 = a1 + 9d
Put this in Equation (1)
we get
5a + 10d = 1/4 ( 5a + 35d )
Put a = 2
we get
30-35 = 5d
Therefore d= -6
Hope you have understand this answer
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Sum of first 5 terms of an A.P. is one fourth of the sum of next five terms. If the first term = 2, then the common difference of the A.P. isa)3b)6c)- 6d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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