Question

in an AP if the 5th and 12th terms are 30 and 65 respectively what is the sum of the first 20 terms

Answer 1

Let first term = a

and common difference = d

T5 = a + ( 5 - 1 ) d

=> a + 4d

T12 = a + ( 12 - 1 ) d

=> a + 11d

A/q

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

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

On solving 1 and 2 we get

a + 4d = 30

a + 11d = 65 } Sub
______________

- 7 d = - 35

=> d = 5

From ( 1 )

a + 4d = 30

=> a + 4 ( 5 ) = 30

=> a + 20 = 30

=> a = 30 - 20

=> a = 10

Here a = 10

d = 5

S20 = n / 2 [ 2a + ( n - 1 ) d ]

=> 20 / 2 [ 2 × 10 + ( 20 - 1 ) 5 ]

=> 10 [ 20 + 19 × 5 ]

=> 10 [ 20 + 95 ]

=> 10 [ 105 ]

=> 1050.

Answer 2

Step-by-step explanation:

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