Question

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

Answer 1

The sum of the given sequence is -24846.

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 ⇒ 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, $n =(\frac{-450-46}{4}) +1$

⇒ $n = (\frac{-496}{4}) + 1$

⇒ $n = -124 + 1$

⇒ $n = -123$

⇒ 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 $S = \frac{n}{2}(a_{1} + a_{n} )$

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, $S = \frac{123}{2}(46+ (-450))$

⇒ $S = \frac{123}{2}(-404)$

⇒ $S = 123 \times -202$

⇒ $S = -24846$

∴ The sum of the given sequence is -24846.