Question

Find the sum of 46 + 42 +38... +(-446) +(-450)

Answer 1

The sum of the given sequence is -24846.

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 ⇒ 46 - 42 = 4

To find the number of terms in the sequence :

The formula used is
`n = (\frac{a_(n)-a_(1)} {d})+1`

where,

• n is the number of terms.
• 
  `a_(n)` is the late term which is -450.
• 
  `a_(1)` is the first term which is 46.
• d is the common difference which is 4.

Therefore,
`n =((-450-46)/(4)) +1`

⇒
`n = ((-496)/(4)) + 1`

⇒
`n = -124 + 1`

⇒
`n = -123`

⇒ n = 123, since n cannot be negative.

∴ The number of terms, n = 123.

To find the sum of the arithmetic progression :

The formula used is
`S = (n)/(2)(a_(1) + a_(n) )`

where,

• S is the sum of the sequence.
• 
  `a_(1)` is the first term which is 46.
• 
  `a_(n)` is the late term which is -450.

Therefore,
`S = (123)/(2)(46+ (-450))`

⇒
`S = (123)/(2)(-404)`

⇒
`S = 123 * -202`

⇒
`S = -24846`

∴ The sum of the given sequence is -24846.