Question

find the sum of the following aps -37,-33,-29.....,to12terms

Answer 1

this sequence is in AP .
here, d= -33-(-37)= 4
a= -37
n=12
:. S= n/2[2a+(n-1)d]
= 12/2[-74+(11)4]
= 6(-74+44)
= 6(-30)
= -180

Answer 2

a= -37

d= a2 - a1

d= -33 - (-37)

d= -33 + 37

d= 4

n = 12

$\green→Sn = \frac{n}{2} (2a + (n - 1)d) \\ \green→Sn =\frac{12}{2} (2\times(-37) + (12 - 1)\times4) \\ \green→ Sn = \frac{12}{2} ( - 74 + 11 \times 4) \\ \green→Sn = 6( - 74 + 44) \\ \green→Sn = 6 \times ( - 30) \\ \green→ \red{Sn = - 180}$