Question

t1=13,tn=216,d=7 then find the sum of all terms

Answer 1

the answer of this question is
it is hint for you

Answer 2

Here is the solution :

Given that,

t1 = 13, ----- 1st term ( a )

tn = 216, -------- last term (a + (n-1)*d)

d = 7, ---------- Common difference

Our Aim :

[1] To find no. of terms,

[2] Sum of all terms !.

Let's accomplish 1 first,

In general, Nth term of an A.P is of form a + (n-1)d,

So from this we can write this,

216 = 13 + (n-1)*7,

=> 203 = (n-1)*7,

=> 29 = (n-1)

=> 30 = n

Therefore : Total 30 numbers are there in the given A.P,

Now Aim 2 :

In general Sum of all terms of an A.P is given by ,

(n/2)*(a+l),

Where l = last term of A.P,

a = First term of A.P,
n = No.of terms of an A.P,


=> Sum of terms of the given A.P is,

(30/2)*(13+216)

=> (15)*(229)

=>3435,

Therefore : Sum of all terms of the given A.P is 3435,


Hope you understand, Have a Great day !.
Thanking you Bunti 360 !.