Question

the sum of the fifth and ninth terms of an Ap is 40 and
that
of eighth and fourteenth term is 64, Find the sum
of first twenty terms​

Answer 1

Answer:

Solve : Given -

sum of 5th and 9th term of Ap = 40

sum of 8th and 14th term of Ap = 64

find sum of first twenty term

=5th term of Ap -

a5 = a + (5-1)d.

a5 = a + 4d

=9th term of Ap-

a9 = a + (9-1)d

a9 = a + 8d

a5 + a9 = 40.

= a + 4d + a + 8d = 40

= 2a + 12d = 40....................... eq - 1.

=8th term of Ap-

= a8 = a + (8-1)d

= a8 = a + 7d

=14th term of Ap-

= a14 = a + (14-1)d

= a14 = a+ 13d

a8 + a14

a + 7d + a + 13d = 64

2d + 20d = 64.......................eq- 2

= Substract eq 1 from 2

2a + 20d = 64

2a + 12d = 40

- - -

____________

8d = 24

d = 24/4. = d = 3

puting the value of d in eq 1

2a + 12d = 40

2a + 12(3) = 40

2a + 36 = 40

2a = 40 -36

2a = 4. = a = 4/2. a = 2

Then,

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

s20 = 20/2[ 2(2) + (20 -1)(3)]

s20 = 10 [4+19(3)]

s20 = 10[4+ 57]

s20 = 10[61]

s20 = 610. Ans.