–20, –16, –12, –8, –4, . . . What is the the sum of the first 30 terms of the sequence?

Step-by-step explanation:

This is an arithmetic sequence because each term subtracted by the previous term is a constant called the common difference.

an=a+d(n-1) where a is the initial term and d is the common difference

a=-20 and d=-16+20=4 so

an=-20+4(n-1)

an=4n-24

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms

sn=(a1+an)(n/2)

s30=(-20+4(30)-24)(30/2)

s30=1140

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐