Question

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

Answer 1

Answer:

$\frac{21n}{2} -\frac{5n^{2} }{2}$

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

a: first term

d: common difference

n : total terms

• by substituting value in the above formula,

• sum of the A.P: $\frac{n}{2} [2(8)+(n-1)-5]$

$\frac{n}{2} [16+(n-1)(-5)]$

$\frac{n}{2} [16+(n-1)(-5)]$

$\frac{n}{2} [16+-5n+5]$

$\frac{n}{2} [21+-5n]$

=$\frac{21n}{2} -\frac{5n^{2} }{2}$