Question

Find 3+6+9+ ... + 180.

• A. 5490
• B. 4950
• C. 5400
• D. ഇതൊന്നുമല്ല

Answer 1

Answer:

A. 5490

 3+6+9+ ... + 180 can be considered as an arithmetic series. 

· First term, a = 3 

· Last term, t_n = 180 

· Common difference, d = 2^nd term – 1^st term 

= (6-3) 

= 3 

· Number of terms, n = ? 

 

 To find the number of terms, we can use the formula to find the last term
t_n
= a + (n-1) d  

180 = 3
+ (n-1) 3 

180 = 3
+ 3n – 3 

180 = 3n
 

3n = 180 

n = 180/3 

n = 60 

 

To find the total sum of the terms in an arithmetic
series, 

S_n
= n/2 [2a + (n-1)d] 

= 60/2 [(2x3)+(60-1)3] 

= 30 [6+(59x3)] 

= 30 x (6+177) 

= 30 x
183 

= 5490