Question

Find the sum of the Arithmetic Series upto 36 terms

2, 5, 8, 11,...
A) 3924
B) 1962
C) 1684
D) 1452

Answer 1

Answer:   B) 1962 


That is given by Sn = n(a1 + an)2Sn = n(a1 + an)2 Where n =number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + (n−1)dan = a1 + n-1d where d =common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, an= a1 + (n − 1)d a36= 2 + (36 − 1)3 = 105 + 2 = 107 an= a1 + n - 1d a36= 2 + 36 - 13 = 105 + 2 = 107 

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.

Answer 2

Q:

Find the sum of the Arithmetic Series upto 36 terms
2, 5, 8, 11,...

A) 3924
B) 1962
C) 1684
D) 1452

Answer:   B) 1962 

Read Description :

Arithmetic Series ::
 
An Arithmetic Series is a series of numbers in which each term increases by a constant amount.
 
How to find the sum of the Arithmetic Sequence or Series for the given Series ::
 
When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.
 
That is given by Sn = n(a1 + an)2 Where n = number of terms, a1 =first term, an = last term
 
Here Last term is given by an = a1 + (n-1)d where d =common difference
 
Now given Arithmetic Series is 
 
2, 5, 8, 11,...
 
Here a1 = 2,  d = 3, n = 36 
 
Now, an= a1 + (n - 1)d 

a36= 2 + (36 - 1)3 = 105 + 2 = 107 
 
Now, Sum to 36 terms is given by
 
S36 = 36(2 + 107)/2 = 36 x 109/2 = 3924/2 = 1962
 
 
 
Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.