Question

Find the sum to $n$ terms of the A.P $5,2,-1,-4,-7,.....$

Answer 1

Given A.P is

$5,2,-1,-4,-7,...\dots ..$

number of terms of A.P is $n$

first term of this A.P is $a_1=5$

second term of this A.P is $a_2=2$

common difference

$d=a_2-a_1=2-5=-3$

we know that sum of n term of an A.P is given by

$S_n=\frac{n}{2}[2a+(n-1)d)]$

$⟹S_n=\frac{n}{2}[2\times 5+(n-1)\times -3)]$

$⟹S_n=\frac{n}{2}[10-3n+3)]$

hence the sum of n terms of given A.P is .

$⟹S_n=\frac{n}{2}[13-3n]$