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The sum of the first six terms of an AP is 42. The ratio of 10th term to the 30th term of AP is ⅓. Calculate the 1st term and 18th term |
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Answer» Answer: Step-by-step explanation: SUM of the FIRST n terms is given by S n
= 2 n
[2a+(n−1)d] S 6
= 2 6
[2a+(6−1)d] S 6
=3[2a+5d] T 30
T 10
= 3 1
a+29d a+9d
= 3 1
(a+9d)3=(a+29d)1 3a+27d=a+29d 2a=2d a=d...(1) S 6
=3[2a+5d] S 6
=3[2a+5a] 42=3(7a) 42=21a ∴a=2 From (1) d=a=2 T 13
=a+(n−1)d =2+(13−1)2 =2+24 =26 |
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