Question

Find the sum of the A.P:8,-3,-2,-7,-12....up to n terms​

Answer 1

`(21n)/(2) -(5n^(2) )/(2)`

Explanation:

• given ap series : 8,3,-2,-7,-12....up to n terms​

[the second term should be +3 or else it wont form AP series]

first term in the series: 8

common difference : 3-8 = -5

total terms : n

• the formula for sum of n terms in an ap =
  `(n)/(2) [2a+(n-1)d]`

a: first term

d: common difference

n : total terms

• by substituting value in the above formula,

• sum of the A.P:
  `(n)/(2) [2(8)+(n-1)-5]`

`(n)/(2) [16+(n-1)(-5)]`

`(n)/(2) [16+(n-1)(-5)]`

`(n)/(2) [16+-5n+5]`

`(n)/(2) [21+-5n]`

=
`(21n)/(2) -(5n^(2) )/(2)`