Question

Find the sum of each arithmetic series

1). 38+35+32+......+2

Answer 1

Solution:

First we have to know that how many terms are there in the above series.
since it is an Arithmetic Series

let a be the first term
d be the common difference
L be the last term
n will be the number of terms present

a = 38 d = t₂ - t₁ L = 2

d = 35-38

= -3

now as we know

nth term(L) = a + (n-1)d

here we are taking the last term (which is given in question L = 2 )

From this we have to find n

L - a = (n - 1)d

n - 1 = (L - a )/d

now

n = [(L-a)/d] + 1

substituting the Values
which are foundout

= [(2-38)/(-3)] + 1

= [(-36)/(-3)] + 1

= 12 + 1

n = 13

so we got the number of terms n

so sum of n terms Here n is found to be 13 ,
so Sum of 13 terms

Sn = (n/2)(first term+last term)

here first term = a
last term = L
​​​Substitute the Values Which are found

Sn = (n/2) (a+L)

= (13/2) (38 + 2)

= (13/2) (40)

= (13) (20)

= 260 (AnswerAnswer)