Question

for an AP the first term is 4 and the last term is tn is 31 the sum of all the terms is 420 what is the value of n???​

Answer 1

Step-by-step explanation:

Given:-

The first term is 4 and the last term is tn is 31 the sum of all the terms is 420 in an AP.

To find:-

what is the value of n?

Solution:-

The first term of an AP=(a)=4

The Last term of the AP=(tn)=31

Sum of all the terms =420

Let the number of terms in the given AP be "n"

Sum of "n" terms=Sn=420

We know that

Sn=n(a+tn)/2

=>n(4+31)/2=420

=>n(35)/2=420

=>35n/2=420

=>35n=420×2

=>35n=840

=>n=840/35

=>n=24

Number of terms=24

Answer:-

The value of "n" in the given AP=24

Used formulae:-

"a" is the first term and the common difference is "d" and number of terms is "n" of an AP then,

• General term or nth term=tn=a+(n-1)d
• Sum of n terms Sn=(n/2)[2a+(n-1)d] or
• Sn=(n/2)(a+tn) or Sn=(n/2)(a+l)

Here, l or tn is the Last term

Answer 2

Step-by-step explanation:

Given:-

The first term is 4 and the last term is tn is 31 the sum of all the terms is 420 in an AP.

To find:-

what is the value of n?

Solution:-

The first term of an AP=(a)=4

The Last term of the AP=(tn)=31

Sum of all the terms =420

Let the number of terms in the given AP be "n"

Sum of "n" terms=Sn=420

We know that

Sn=n(a+tn)/2

=>n(4+31)/2=420

=>n(35)/2=420

=>35n/2=420

=>35n=420×2

=>35n=840

=>n=840/35

=>n=24

Number of terms=24

Answer:-

The value of "n" in the given AP=24

Used formulae:-

"a" is the first term and the common difference is "d" and number of terms is "n" of an AP then,

General term or nth term=tn=a+(n-1)d

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

Sn=(n/2)(a+tn) or Sn=(n/2)(a+l)

Here, l or tn is the Last term