Question

6. Determine the sum of the first 75 terms of the sequence 4, 1, -2, -5, -8,...

Answer 1

SOLUTION;

the series number is

P= 4,1,-2,-5,-8,........

a= 4 =first number

d= different between two corresponding number

d= 1-4=-2-1=-5-(-2)=........=-3

And fund first 75 number sum so

n=75

We know that, sum of n first number of series is

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

S75 75. [2a + (75-1) 2

$S_{75}=\frac{75}{2}[2(4)+(75-1)(-3)]$

$S_{75}=\frac{75}{2}[8+(74)(-3)]$

$S_{75}=\frac{75}{2}(-214)$

$\therefore S_{75}=-8025$

The sum of first 75 number is $S_{75}=-8025$

Answer =-8025