Question

in an Ap if the 5th term and 12th terms are 30 and 65 respectively then the sum of first 20 terms is​

Answer 1

Answer:

1115 therefore the sum of frist 20 numbers

Answer 2

Answer:

1150

Step-by-step explanation:

tn = a + (n - 1)d

:. t5 = a + (5 - 1)d

:. 30 = a+4d ..... (i)

:. t12 = a + (12 - 1)d

:. 65 = a + 11d ..... (ii)

Subtracting eq. (i) from (ii)

65 - 30 = a + 11d - (a + 4d)

:. 35 = a + 11d - a - 4d

:. 35 = 7d

:. d = 35/7

:. d = 5 ...... (iii)

From eq. (iii) and (i) ,

a + 4d = 30

:. a + 4(5) = 30

:. a + 20 = 30

:. a = 10

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

S20 = 20/2 [ 2(10) + (20 - 1)5 ]

= 10 [ 20 + 19(5) ]

= 10 [ 20 + 95 ]

= 10 x 115

= 1150