Question

the 7th and the 9th term of an ap are 15 and 27 respectively. find the series and the sum of the first 50 terms​

Answer 1

Step-by-step explanation:

an = a +(n-1) d

15 = a +( 7 -1 ) d

15 = a + 6 d ............(1)

an = a + (n-1) d

27 = a + ( 9- 1) d

27 = a + 8 d .............(2)

By solving (1) and(2) with elimination method you get

15 =a +6d

27 = a + 8d

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- 12= -2d

therefore d =6

15= a +6d

15 = a + 6 ( 6)

15= a +36

15 - 36 =a

-21= a

AP = -21 , -15 , -9 .......

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

=50/2 ( 2 (-21) + ( 50-1) (6))

= 25( -42+(49)(6))

= 25 (-42+294)

=25(252)

= 6300