Question

if the n' term of an A.P is tn=3-5n then the sum of the first in term is​

Answer 1

Answer:

(-5n2+n)/2

Step-by-step explanation:

tn=3-5n

put n=1

3-5=-2

n=2

3-10=-7

n=3

3-15=-12

d=-7+2=5

Answer 2

Step-by-step explanation:

we have given, nth term (tn = 3-5n) of an AP

by the nth term, let's find out a( first term) and d (common difference)

t(1) = 3 - 5(1) = 3 - 5 = -2

t(2) = 3 - 5(2) = 3 - 10 = -7

t(3) = 3 - 5(3) = 3 - 15 = -12

t2-t1 = -7-(-2) = -5, t3-t2=-12-(-7) = -5

so the first term a = -2 , common difference is d = -5

Now, we know, Sn =( n/2)(2a + (n-1)d)

put the values of a and d in the formula for Sn

Sn = (n/2) (2(-2)+(n-1)(-5))

= (n/2) (-4 + (n-1) (-5))

= (n/2) (-4 +(-5n+5))

= (n/2)(-5n + 1)

= [(-5n²/2 ) + (n/2)]