Question

what is the sum of first n odd natural number starting from 11 (a) n2+10n (b) n2-10n (c) 10n-n2 (d) n2​

Answer 1

Answer : (a) n² + 10n

$\bf\huge\underline{\underline{ To \: Find:- }}$

• sum of n odd natural numbers starting from 11

$\bf\huge\underline{\underline{ Answer :- }}$

• sum of odd natural numbers starting from 1

• $\red{\implies}$ n²

• general formula of odd numbers = 2n - 1

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On starting from 11 ,

• 1st term = 11

• difference = 2

• $\boxed { \red{algebraic \: formula = dn +( f - d )}}$

• $\red{\implies}$ algebraic formula = 2n + (11-2)

• $\red{\implies}$ algebraic formula = 2n + 9

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Sum of terms ,

• $\bf\red{Sum = \frac{n}{2} ×(t_{1} + t_{n} ) }$

• $\bf\red{\implies} \:\bf sum \: = \frac{n}{2} \times (11 + 2n + 9)$

• $\bf\red{\implies} \: sum \: = \: \frac{n}{2} \times (2n + 20)$
• $\bf\red{\implies} \: \: \frac{2( {n}^{2} + 10n) }{2}$

• $\bf\red{\implies} \: \: {n}^{2} + 10n$

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ie , Sum of n odd terms starting

from 11 is n² + 10n

Answer 2

n² + 10 n i think so

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