Question

Find the sum of first 25 terms of an AP whose n th term is 2-3n
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Answer 1

Answer:

925

Step-by-step explanation:

Given :t_n = 2 - 3nt

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 - 3nt

n

=2−3n

Put n =1

t_1 = 2 - 3(1)t

1

=2−3(1)

t_1 = -1t

1

=−1

put n =2

t_2 = 2 - 3(2)t

2

=2−3(2)

t_2= -4t

2

=−4

put n =3

t_3 = 2 - 3(3)t

3

=2−3(3)

t_3= -7t

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 : \frac{n}{2}(2a+(n-1)d)

2

n

(2a+(n−1)d)

Put n =25

\frac{25}{2}(2(-1)+(25-1)(-3))

2

25

(2(−1)+(25−1)(−3))

\frac{25}{2}(-2-72)

2

25

(−2−72)

\frac{25}{2}(-74)

2

25

(−74)

-925−925

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

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