If 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ, find the value of c

Solution:

Given, the expression is 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ.

We have to find the value of c.

For any non-zero integers ‘a’ and ‘b’ and whole numbers m and n,

a^m × aⁿ = a^m+n

So, 2^{n + 2} = 2ⁿ × 2²

2^{n + 1} = 2ⁿ × 2¹

Now, 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ

(2ⁿ × 2²) - (2ⁿ × 2¹) + 2ⁿ = c × 2ⁿ

Taking common term 2ⁿ,

2ⁿ(2² - 2 + 1) = c × 2ⁿ

Cancelling out common term,

2² - 2 + 1 = c

c = 4 - 2 + 1

= 4 - 1

= 3

Therefore, the value of c is 3.

✦ Try This: A drop of water of 1.8 gm weight has 60,230,000,000,000,000,000,000 molecules. Express it in standard form

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 13

NCERT Exemplar Class 7 Maths Chapter 11 Problem 90

If 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ, find the value of c

Summary:

If 2ⁿ⁺² - 2ⁿ⁺¹ + 2ⁿ = c × 2ⁿ, the value of c is 3

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