Question

for an A. P.,Sn=860,T1=2,Tn=41,Then find n​

Answer 1

Step-by-step explanation:

Given :-

Sn = 860

Sn = 860t1 = 2

Sn = 860t1 = 2tn = 41 of an AP

To find :-

Find the value of n ?

Solution :-

Method-1:-

Given that

In an AP,

Sn = 860

t1 = 2

tn = 41

We know that

The sum of first n terms of an AP

(Sn)= (n/2)[t1+tn]

On substituting these values in the above formula

=> 860 = (n/2)(2+41)

=> 860 = (n/2)(43)

=> 860 = (n×43)/2

=> 860 = 43n/2

=> 43n/2 = 860

=> 43n = 860×2

=> n = 860×2/43

=> n = 20×2

=> n = 40

Number of terms in the AP = 40

Method-2:-

Given that

In an AP,

Sn = 860

t1 = 2

tn = 41

We know that

nth term of the AP = tn = t1 +(n-1)d

=> 41 = 2 +(n-1)d

=> 41-2 = (n-1)d

=> 39 = (n-1)d --------(1)

The sum of first n terms of an AP (Sn)

= (n/2)[2t1+(n-1)d]

=> 860 = (n/2)[2(2)+(n-1)d]

=> 860 = (n/2)[4+(n-1)d]

=> 860 = (n/2)(4+39) (from (1))

=> 860 = (n/2)(43)

=> (n/2)(43) = 860

=> n/2 = 860/43

=> n/2 = 20

=> n = 20×2

=> n = 40

Number of terms in the AP = 40

Answer:-

The value of n for the given AP is 40

Used formulae:-

→ nth term of the AP = tn = t1 +(n-1)d

→ The sum of first n terms of an AP (Sn)

= (n/2)[2t1+(n-1)d]

→ The sum of first n terms of an AP (Sn)

= (n/2)[t1+tn]

• t1 = first term
• d = common difference
• n = number of terms

Answer 2

Answer:

use the formula

$\frac{n}{2} (a + l)$

put the value and you'll get the answer.