Respuesta :

sum of sequence Find the sum of 46 + 42 + 38 + ... + (-446) + (-450) is -25,250

Step-by-step explanation:

We need to find sum of sequence  : 46 + 42 + 38 + ... + (-446) + (-450)

Given sequence is an AP with following parameters as :

[tex]a=46\\d=42-46=-4[/tex]

So , Let's calculate how many terms are there as :

⇒ [tex]a_n=a +(n-1)d[/tex]

⇒ [tex]-450=46 +(n-1)(-4)[/tex]

⇒ [tex]-496=(n-1)(-4)[/tex]

⇒ [tex]\frac{-496}{-4}=n-1[/tex]

⇒ [tex]124=n-1[/tex]

⇒ [tex]n=125[/tex]

Sum of an AP is :

⇒ [tex]S_n = \frac{n}{2}(2a+(n-1)d)[/tex]

⇒ [tex]S_1_2_5 = \frac{125}{2}(2(46)+(125-1)(-4))[/tex]

⇒ [tex]S_1_2_5 = \frac{125}{2}(-404)[/tex]

⇒ [tex]S_1_2_5 =-25,250[/tex]

Therefore , sum of sequence Find the sum of 46 + 42 + 38 + ... + (-446) + (-450) is -25,250

bhuvna789456

The sum of the given sequence is -25500.

Step-by-step explanation:

The given Arithmetic sequence is 46 + 42 +38... +(-446) +(-450).

  • The first term of the sequence = 46
  • The last term of the sequence = -450
  • The common difference ⇒ 42 - 46 = - 4

To find the number of terms in the sequence :

The formula used is [tex]n = (\frac{a_{n}-a_{1}} {d})+1[/tex]

where,

  • n is the number of terms.
  • [tex]a_{n}[/tex] is the late term which is -450.
  • [tex]a_{1}[/tex] is the first term which is 46.
  • d is the common difference which is 4.  

Therefore, [tex]n =(\frac{-450-46}{-4}) +1[/tex]

⇒ [tex]n = (\frac{-496}{-4}) + 1[/tex]

⇒ [tex]n = 124 + 1[/tex]

⇒ [tex]n =125[/tex]

∴ The number of terms, n = 125.

To find the sum of the arithmetic progression :

The formula used is [tex]S = \frac{n}{2}(a_{1} + a_{n} )[/tex]

where,

  • S is the sum of the sequence.
  • [tex]a_{1}[/tex] is the first term which is 46.
  • [tex]a_{n}[/tex] is the late term which is -450.

Therefore, [tex]S = \frac{125}{2}(46+ (-450))[/tex]

⇒  [tex]S = \frac{125}{2}(-404)[/tex]

⇒ [tex]S = 125 \times -202[/tex]

⇒ [tex]S = -25500[/tex]

∴ The sum of the given sequence is -25500.

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