Question

20. In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?​

Answer 1

Step-by-step explanation:

a+4d=30

a+11d=65

a+11d - a-4d=35

7d=35

d=5

a+20=30

a=10

s20 = n/2(2a+(n-1)d)

=20/2(20 + 95)

= 10(115)

= 1150

Answer 2

GIVEN :

5th term of an AP = 30

a + 4d = 30 ------(1)

12th term of an AP = 65

a + 11d = 65 ------(2)

Solve eq - 1 & 2 to find Common difference (d).

a + 4d = 30

a + 11d = 65

(-)

-------------------

-7d = -35

d = 35/7

d = 5

Common Difference = 5

Now, Substitute d in eq - (1) to find first term (a)

a + 4d = 30

a + 4(5) = 30

a + 20 = 30

a = 30 - 20

a = 10

First Term = 10

In an AP sum of the terms = n/2 ( 2a + (n - 1)d

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

= 20/2 ( 2(10) + (20 - 1)5

= 10 ( 20 + (19)5 )

= 10 ( 20 + 95)

= 10 ( 115)

= 1150

Therefore, the sum of first 20 terms = 1150.

Hope it help