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The 19th term of an AP …

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The 19th term of an AP is equal to three times its sixth term.if its 9th term is 19,find the AP
  • 2 answers

Gaurav Seth 6 years, 10 months ago

<form action="https://www.sarthaks.com/154176/the-19th-term-of-an-ap-is-equal-to-3-times-its-6th-term-if-its-9th-term-is-19-find-the-ap" method="post">

Let a be the first term and d be the common difference of the AP. Then,

</form>

Pranav Songra 6 years, 10 months ago

a19=3(a6) a9=19 a+8d=19 a=19-8d .......(1) a19=3(a6) a+18d=3(a+5d) a+18d=3a+15d 18d-15d=3a-a 3d=2a 3d=2(19-8d) ........(from 1) 3d=38-16d 3d+16d=38 19d=38 d=38/2 d=2. ......(2) Put d=2 in eq.1 a=19-8×2 a=3 now put values of a &d in above equation a19=3(a6) a+18d=3(a+5d) 3+18×2=3(3+5×2) 3+36=3(3+10) 39=9+30 39=39 .•. AP= 3,5,7...... H.P. Hope this helps.? Regards
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