Question

Find the sum of 14 + 8 + 2+ ... + ( 274) + (-280).

Answer 1

The sum of the given sequence is -6384.

Step-by-step explanation:

The given Arithmetic sequence is 14 + 8 + 2+ ... + ( 274) + (-280).

• The first term of the sequence = 14
• The last term of the sequence = -280
• The common difference ⇒ 14 - 8 = 6

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 -280.
• $a_{1}$ is the first term which is 14.
• d is the common difference which is 6.

Therefore, $n =(\frac{-280-14}{6}) +1$

⇒ $n =( \frac{-294}{6}) + 1$

⇒ $n = -49 + 1$

⇒ $n = -48$

⇒ n = 48, since n cannot be negative.

∴ The number of terms, n = 48.

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 14.
• $a_{n}$ is the late term which is -280.

Therefore, $S = \frac{48}{2}(14+ (-280))$

⇒ $S = \frac{48}{2}(-266)$

⇒ $S = 48 \times -133$

⇒ $S = -6384$

∴ The sum of the given sequence is -6384.