Question

71+72+73+74+75+76+77+78+79+80=?
answer this quition without adding and then explain why this answer is correct for this question​

Answer 1

Answer:

• Sum of all terms = 755

Explanation:

We have been given an expression, 71+72+73+74+75+76+77+78+79+80.

{ There are two method to solve such questions }.

Method:1 { Arithmetic Progression}

71+72+73+74+75+76+77+78+79+80.

• First term , a = 71
• last term = 80
• Number of terms , n = 10

So, We have to find the summation of given AP.

→ Sn = n/2(a + l)

→Sn = 10/2(71+80)

→Sn = 5 ( 151)

→Sn = 755

• Therefore, The required summation of AP is 755.

Method : 2 { Direct Addition}

→ 71+72+73+74+75+76+77+78+79+80.

→ 755

Answer 2

71+72+73+74+75+76+77+78+79+80 = ?

Here ..

• First term (a) = 71

• Common difference (d) = $a_{2}\:-\:a_{1}$

=> 72 - 71 = 1

• Last term $(a_{n})$ = 80

• Number of terms (n) = 10

___________________ [ GIVEN ]

• We have to find the sum of the above numbers without adding.

Means $S_{n}$

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Now ..

› We know that

=> $S_{n}$ = $\dfrac{n}{2}$ (a + $a_{n})$

→ $S_{n}$ = $\dfrac{10}{2}$ (71+ 80)

→ $S_{n}$ = 5 (151)

→ $S_{n}$ = 755

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$\huge{ \bold{S_{n} \: = \: 755}}$

_____________ [ ANSWER ]

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