Question

find the sum of first 81 term of an ap whose 2nd and 3rd term are 16 and 21​

Answer 1

Step-by-step explanation:

A2= a+d =16

A3 =a+3d= 21

now subtract both the equation

= -2d =-5

= d=2.5

a= 16-2.5=13.5

A81= 13.5+ 80*2.5

= 13.5 +200

=213.5

Answer 2

Given

Second term is 16

third term is 21

To Find

We have to find the sum of first 81 term of am ap

$\sf\huge \mathbb{\underline{\underline{{Solution}}}}$

Since ,we don't know the first term (a) and the common difference (d).So,with the given terms we will find a and d.

2nd term can also be written as => a+d

So,a+d=16----(1)

Third term can also be written as=>a+(3-1)d

=> a+2d

a+2d =21------(2)

Now, writing both Equation 1 and 2

a+2d=21

a+d=16

Substracting Equation 1 from 2

➙a+2d=21

➙a+d=16

➙$(-)(-)\:(-)$

___________

2d-d=21-16

d= 5

Put d's value into equation 1

➙a+d= 16

➙a+5=16

➙a=16-5=11

Therefore, first term is 11 & common difference is 5

We have to find sum of first 81 terms

formula for finding the sum :

Sₙ= n/2[2a+(n-1)d]

S₈₁= 81/2[2(11)+(81-1)5]

S₈₁=81/2[2(11+80(5)]

S₈₁=81/2( 22+400)

S₈₁=81/2(422)

S₈₁=81×211

S₈₁=17091

Hence,the sum of first 81 term is 17091