Question

What is the sum of the first forty terms of the arithmetic sequence 120, 115, 110, 105....?

• A. 900
• B. 700
• C. 500
• D. 300

Answer 1

The correct option is A 900

The sum of $n$ terms of an arithmetic sequence can be calculated by $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
Where,$n$ denotes the total number of terms
$a=$ first term
$d=$ common difference
$S_n=$ Sum of $n$ terms

$\therefore$ First Term: $a=120$

Common Difference: $d=-5$

Total terms: $n=40$

Sum of $40$ terms:

$S=\frac{40}{2}\times (2\times 120+(40-1)\times (-5\left)\right)$

$S=20\times (240-39\times 5)$

$S=900$