Question

if the sum of the 1st a terms of an Ap is 4n-n². what is the 1st
term? what is the sum of 1st two terms?
​

Answer 1

Answer :

In these types of questions if we are given any sum in the term such as n etc. We have to put n = 1 and then note the values and put n = 2 for common difference. I will be using this method in above question :

Given

Sn = 4n - n²

Put n = 1

S1 = 4(1) - (1)²

S1 = 4 - 1

S1 = 3

∴ Sum of first term is 3

As we know that sum of 1st term is the first term itself.

So, a = S1

$\rule{200}{2}$

For sum of first two terms put n = 2

S2 = 4(2) - (2)²

S2 = 8 - 4

S2 = 4

∴ Sum of first two terms is 4

Answer 2

$\huge\underline\mathrm{Correct\:Question-}$

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If the sum of the 1st n terms of an Ap is 4n-n². what is the 1st term? what is the sum of 1st two terms?

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$\huge\underline\mathrm{Answer-}$

⠀

$\large{\boxed{\red{a=3}}}$

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$\large{\boxed{\red{S_2=4}}}$

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$\huge\underline\mathrm{Explanation-}$

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Given :

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• $\tt{S_n=4n-n^2}$

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To find :

• $\tt{First\:term\:i.e\:a}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀
• $\tt{Sum\:of\:first\:two\:terms\:i.e\:S_2}$

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Solution :

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Put n = 1

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$\implies$ $\tt{S_1=4(1)-(1)^2}$

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$\implies$ $\tt{S_1=4-1}$

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$\implies$ $\tt{S_1=3}$

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Also, $\tt{a=S_1}$

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$\large{\boxed{\red{\therefore\:a=3}}}$

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Similarly, put n = 2 to know about the sum of two terms.

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$\implies$ $\tt{S_2=4(2)-(2)^2}$

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$\implies$ $\tt{S_2=8-4}$

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$\implies$ $\tt{S_2=4}$

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$\large{\boxed{\red{\therefore\:S_2=4}}}$

$\rule{200}1$