Question

if 5 times the 5th term of an A.P is equal to the 8times its 8th term shows that its 13th term is zero
OR
if the nth term of an A.P is 7-3n,find the sum of twenty five terms

Answer 1

5(a + 4d) = 8(8 + 7d)

5a + 20d = 8a + 56d

8a - 5a = 20d - 56d

3a = - 36d

a = - 12d

a + 12d = 0

Thus 13th term is 0

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Answer 2

Answer:

Step-by-step explanation:

Let the first term of the A.P.=

a and common difference =d

5×5Tth term=8×8Tth term

5(a+(5-1)d)=8{a+(8-1)d}

5a+20d=8a+56d

8a-5a+56d-20d=0

3a+36d=0

3a=-36d

a=-12d

13th term

=a+(13-1)d

=-12d+12d

=0

nth term

=7-3n

Put n=1,2,3,4,.........

A.P 4,1,-2,.......

a=4

d=1-4=-3

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

=5/2[2×4+(5-1)×-3]

=5/2(8-12)

=5/2×-4

=5×-2

=-10