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Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?
and pls pls explain it?
and pls pls explain it?
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Let SN denotes the sum of n terms of an ap whose first term is a if th...
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Let SN denotes the sum of n terms of an ap whose first term is a if th...
Problem:
Let SN denotes the sum of n terms of an AP whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?
Solution:
To find the value of k, we need to use the given formula for the common difference, which is:
D = Sn - kSn-1 + Sn-2
Step 1: Understanding the terms in the formula
Let's break down the terms in the formula:
- Sn represents the sum of n terms of the arithmetic progression.
- Sn-1 represents the sum of (n-1) terms of the arithmetic progression.
- Sn-2 represents the sum of (n-2) terms of the arithmetic progression.
- D represents the common difference of the arithmetic progression.
Step 2: Expanding the terms
Let's expand the terms to get a better understanding:
Sn = a + (a+d) + (a+2d) + ... + (a+(n-1)d)
Sn-1 = a + (a+d) + (a+2d) + ... + (a+(n-2)d)
Sn-2 = a + (a+d) + (a+2d) + ... + (a+(n-3)d)
Step 3: Simplifying the formula
Substituting the expanded terms into the formula for the common difference, we get:
D = (a + (a+d) + (a+2d) + ... + (a+(n-1)d)) - k(a + (a+d) + (a+2d) + ... + (a+(n-2)d)) + (a + (a+d) + (a+2d) + ... + (a+(n-3)d))
Step 4: Simplifying further
Combining like terms, we can simplify the formula to:
D = (a + (a+d) + (a+2d) + ... + (a+(n-1)d)) - k(a + (a+d) + (a+2d) + ... + (a+(n-2)d)) + (a + (a+d) + (a+2d) + ... + (a+(n-3)d))
D = a + (a+d) + (a+2d) + ... + (a+(n-1)d) - ka - kd - k(a+d) - k(a+2d) - ... - k(a+(n-3)d) + a + (a+d) + (a+2d) + ... + (a+(n-3)d)
Step 5: Simplifying further
Combining like terms, we can simplify the formula to:
D = (n-1)a + (n-1)d - k(n-2)a - (k+1)(n-2)d + (n-3)a + (n-3)d
Step 6: Simplifying further and finding the value of k
To find the value of k, we need to equate the common difference to the simplified formula:
D = (n-1)a +
Let SN denotes the sum of n terms of an AP whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?
Solution:
To find the value of k, we need to use the given formula for the common difference, which is:
D = Sn - kSn-1 + Sn-2
Step 1: Understanding the terms in the formula
Let's break down the terms in the formula:
- Sn represents the sum of n terms of the arithmetic progression.
- Sn-1 represents the sum of (n-1) terms of the arithmetic progression.
- Sn-2 represents the sum of (n-2) terms of the arithmetic progression.
- D represents the common difference of the arithmetic progression.
Step 2: Expanding the terms
Let's expand the terms to get a better understanding:
Sn = a + (a+d) + (a+2d) + ... + (a+(n-1)d)
Sn-1 = a + (a+d) + (a+2d) + ... + (a+(n-2)d)
Sn-2 = a + (a+d) + (a+2d) + ... + (a+(n-3)d)
Step 3: Simplifying the formula
Substituting the expanded terms into the formula for the common difference, we get:
D = (a + (a+d) + (a+2d) + ... + (a+(n-1)d)) - k(a + (a+d) + (a+2d) + ... + (a+(n-2)d)) + (a + (a+d) + (a+2d) + ... + (a+(n-3)d))
Step 4: Simplifying further
Combining like terms, we can simplify the formula to:
D = (a + (a+d) + (a+2d) + ... + (a+(n-1)d)) - k(a + (a+d) + (a+2d) + ... + (a+(n-2)d)) + (a + (a+d) + (a+2d) + ... + (a+(n-3)d))
D = a + (a+d) + (a+2d) + ... + (a+(n-1)d) - ka - kd - k(a+d) - k(a+2d) - ... - k(a+(n-3)d) + a + (a+d) + (a+2d) + ... + (a+(n-3)d)
Step 5: Simplifying further
Combining like terms, we can simplify the formula to:
D = (n-1)a + (n-1)d - k(n-2)a - (k+1)(n-2)d + (n-3)a + (n-3)d
Step 6: Simplifying further and finding the value of k
To find the value of k, we need to equate the common difference to the simplified formula:
D = (n-1)a +
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Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it?
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Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it?.
Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let SN denotes the sum of n terms of an ap whose first term is a if the common difference D is given by D=Sn-KSn-1 Sn-2, then k= (A) 1 (B) 2 (C) 3 (D) none?and pls pls explain it?.
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