Question

The sum of first nine terms of an arithmetic sequence with first term 9 is 261 then find algebraic expression of the term of this sequence?

Answer 1

Solution

Sn= n/2[ 2a+(n-1)d]

Where

Sn= sum up to n terms of an AP

n= number of terms of AP

a = first term of AP

d= common difference of AP

Substituting the values

261= 9/2[ 2×9+(9-1) d]

261×2/9= 18+8d

8d= 58-18

d= 5

Therefore nth term

= n/2[ 2×9+(n-1)×5]

= n/2[ 18+5n-5]

= n/2[ 5n+13]

This is the exp of nth term of sequence