Question

The sum of all the ten numbers of an AP is485 of its last term is 71 first term and the common difference of the AP

Answer 1

Please refer to the attachment below. Hope this helps you. (Ps- Excuse my handwriting)

Answer 2

Let sum of all ten numbers= S10
Now, we have two formulas for Sum of n terms = (n/2)(a+l) and (n/2)[2a+(n-1)d]
Using these two formulaswe will solve question
It is given that S10=485
Last term,l= 71

n= number of terms
a= first term
l= last term
d= common difference
Sⁿ= (n/2)(a+l) = 485
Putting values we get


(10/2) (a+71)=485
5(a+71)=485
5a+355=485

5a = 485-355
5a=130
a= 26......(1)


Now, (n/2)[2a+(n-1)d]=Sⁿ=485

485=(10/2)[2*26+(10-1)d]
485= 5(2*26+9d)

(485/5)= 52+9d

52+9d = 97

9d= 97-52

9d= 45

d=5

So, common difference=5 and first term= 26
Hope this helps you