The mathematics of Quadratic equation will be uploaded very soon.

{ n }^{ 2 }+39n-20n-780=0

={ n }(n+39)-20(n+39)=0

(n-20) and (n+39)

This means n=20 and n= -39

Since the number of terms in an A.P can’t be negative, the answer is 20 terms which are there in this A.P

Sum of first n terms of an A.P: Type III question

What is the sum of first 20 terms of an A.P whose nth term can be given by

{ a }_{ n }=17+3n

Solution:

Here we have not been given the first term and the common difference of this A.P which are essentially required to solve the questions given in the A.P.

But we have been given this form { a }_{ n }=17+3n where n is unknown.

So what we can do that we can put n=1 on our own side to solve this incomplete question.

{ a }_{ 1 }=17+3\times 1

{ a }_{ 1 }=20

n=2

{ a }_{ 2 }=17+3\times 2

20=17+6

{ a }_{ 2 }=23

n=3

{ a }_{ 3 }=17+3\times 3

20=17+9

{ a }_{ 3}=26

So, now we have found the three terms of this A.P which are:

20, 23, 26… up to 20 terms

Now we have to find the common difference using this formula

{ a }_{ 2 }-{ a }_{ 1 }={ a }_{ 3 }-{ a }_{ 2 }=c.d for more details click here

Common difference (c.d) = 23 – 20 = 26 – 23 = 3

Now we have the first term { a }_{ 1 }=20 and the common/constant difference =3.

And, the number of first terms of this A.P for which the sum is to be found =20.

Now we can use the formula for finding the sum of first n terms of an A.P: