The third terms of an AP is 7 and the 9th terms of AP exceeds 3 times of the 3rd term by 2. Find the first term and it's common difference and sum of the 20 terms
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Answer:
a= 5/3, d= 8/3 , S(20)= 558 int 2/3
Step-by-step explanation:
since, nth term = a+(n-1)d
where, a = first term, d= common difference
=> 3rd term (a3) = a + 2d= 7. ......... .(1)....given
=> 9nth term (a9)= a+8d= 3×( a+2d)+2.... given
=> a+8d= 3a+6d+2
=> 2a-2d+2= 0
=> a-d+1= 0.............(2)
on substracting from (1) to (2)
=> 3d-1= 7=> d = 8/3
=> from eqn (1)
=> a= 5/3
S(20) = (20/2) [ 2×(5/2)+(20-1) (8/3)]
= 10[ 5+19×8/3]
= 1670 / 3
= 558 integer 2/3
=> sum of 20 terms = 558 whole 2/3
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