Question

In an A.P a=2, an=30, sn=800, n=?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

In an A.P a=2, an=30, sn=800

To find :-

Find the value of n ?

Solution :-

Method-1:-

Given that

In an AP ,

First term (a) = 2

Let the Common difference be d

Let the number of terms be n

nth term of the AP = an = 30

Sum of the first n terms = Sn = 800

We know that

Sum of first n terms in an AP is

Sn = (n/2)[a+an]

=> (n/2)[2+30) = 800

=> (n/2)(32) = 800

=> (32n)/2 = 800

=> 16n = 800

=> n = 800/16

=> n = 50

Therefore, number of terms = 50

Method -2:-

Given that

In an AP ,

First term (a) = 2

Let the Common difference be d

Let the number of terms be n

nth term of the AP = an = 30

Sum of the first n terms = Sn = 800

We know that

nth term of an AP = an = a+(n-1)d

Given that

an = 30

=> a+(n-1)d = 30

=> 2+(n-1)d = 30

=> (n-1)d = 30-2

=>( n-1 )d = 28 ------(1)

=> d = 28/(n-1)---------(2)

and

We know that

Sum of first n terms in an AP is

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

Given that

Sn = 800

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

=> (n/2)[4+(n-1)d] = 800

=> (n/2)(4+28) = 800 (from (1))

=> (n/2)(32) = 800

=> 32n/2 = 800

=> 16n = 800

=> n = 800/16

=> n = 50

Therefore, number of terms = 50

Answer :-

The value of n for the given problem is 50

Check :-

a = 2

an = 30

n = 50

S 50 = (50/2)[2+30]

=> S 50 = (25)(32)

=> S50 = 800

Verified the given relations in the given problem.

Used formulae:-

→ Sum of first n terms in an AP is

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

→ nth term of an AP = an = a+(n-1)d

• a = First term
• d = Common difference
• n = Number of terms