Question

For an A.P. Sn=860, t1=2, tn=41 then find n=?​

Answer 1

Answer:

Here is the solution

Step-by-step explanation:

Given :

Sn =860

t1 = 2

tn = 41 , tn = [a +( n-1 )d ]

and we have find

n =?

SN = n/2 (2a + {n-1}d ) = 860

n/2( 2× 2+ (n-1)d ) = 860

n/2 (tn+t1) = 860

n/2 (41 +2) = 860

n/2 (43) = 860

n = (860 ×2 )/43

n = 40

Answer 2

The value of n is 40

Given : For an A.P. Sn=860, t1=2, tn=41

To find : The value of n.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of n)

Here, we will be using the general formulas of AP.

In this case,

• First term of AP (a) = t1 = 2
• Sum of n number of terms (Sn) = 860
• n th term of the AP (tn) = 41

According to the AP series formula :

n th term of AP = a+(n-1) × d

By, putting the available data, we get :

41 = 2 + (n-1) × d

(n-1) × d = 41 - 2

d = 39/(n-1)

Now, again applying AP series formula :

Sum of n terms = (n/2) × [2a + (n-1) × d]

By, putting the available data, we get :

860 = (n/2) × [(2×2) + (n-1) × 39/(n-1)]

860 = n/2 × (4+39)

n/2 = 860/43

n/2 = 20

n = 40

(This will be considered as the final result.)

Hence, the value of n is 40