Question

If n th term of a A. P. is 7-3n; find the sum of first 25 terms

Answer 1

Answer :

Given that, the n-th term of the A.P. is (7 - 3n)

So, the 1st term
= 7 - 3 (1) = 7 - 3 = 4,

the 2nd term be
= 7 - 3 (2) = 7 - 6 = 1,

and the 25th term be
= 7 - 3 (25) = 7 - 75 = - 68

Common difference
= 2nd term - 1st term
= 1 - 4 = - 3

Thus, the sum of the first 25 terms of the A.P. is
= (25/2) * (1st term + 25th term)
= (25/2) * (4 - 68)
= (25/2) * (- 64)
= 25 * (- 32)
= - 800

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Answer 2

Answer:

Step-by-step explanation:

nth term = 7-3n

1st term = 7-3(1)

=7 - 3 = 4

2nd term = 7-6 = 1

a = 4

d = a2 - a1 ​

= 1 - 4 = -3

A.P. = a,a + d, a+2d, a+3d

= 4, 1, 4 + 2 (-3), 4 + 3(-3)

=4, 1, 4-6, 4-9

= 4, 1, -2, -5

Sn=n/2(2a+n-1)d

=25/2(2*4+24*(-3)

=25/2(-64)

= -800