Question

Find the sum of the first 25 terms of an A.P whose nth term is given by tn=2-3n​

Answer 1

Answer:

-925

Step-by-step explanation:

Given :t_n = 2 - 3n

To Find: Find the sum of first 25 terms of an AP whose nth term is given by tn = 2 - 3n

Solution:

t_n = 2 - 3n

Put n =1

t_1 = 2 - 3(1)

t_1 = -1

put n =2

t_2 = 2 - 3(2)

t_2= -4

put n =3

t_3 = 2 - 3(3)

t_3= -7

So, A.P. become s: -1 , -4 , -7, ........

So, first term =a= -1

Common difference d = -4-(-1)=-7-(-4)= -3

Formula of sum of first n terms : n/2(2a+(n-1)d)

(2a+(n-1)d)Put n=25

25/2(2(-1))+(25-1)(-3))

25/2(-2-72)

25/2(-74)

(-74)-925

(-74)-925Hence the sum of first 25 terms of an AP is -925

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Answer 2

formula;

sn=n(a+l)/2

for finding first term we have to use n as1 and substitute in the equation given;

=2-3(1)=-1

for finding last term substitute n as 25;

=2-3(25)=-73

now applying it in the formula,

sn=25(-1-73)/2

=25×-37

=-925