 Hello and welcome to another session on problem solving on sequence and series and we are discussing general term of a sequence Okay, so the question says if five times the fifth term of an AP is equal to eight times its eighth term So that it's 13th term is zero. So don't get intimidated by the language Language at times will be a little difficult, but then you know, you can again Read the question so that all the data what you are Gathering should be correct. Okay, so if five times the fifth term Of an AP is equal to eight times the eighth term. So you can you know very well say that five times The fifth term that is five times T five is equal to eight times T It okay, and you have to find out T13 and you have to show that T13 is zero to show Okay, so you'll say let the first term let the first term of the given AP first of first term of an AP of this AP that is given AP be a right and and Common difference common difference. There are two parameters in AP. You know that which is vital Common difference common difference is Is D? Correct common difference is D. Okay, you have to say this then P five, you know fifth term is nothing but a plus five minus one D Correct, so hence it is a plus four D Right and then T what eight is equal to a plus eight minus one D that is a plus seven D Correct. Now if that is so then by this equation here, we can write five times T five So what is T five guys a plus four D? right is equal to eight times T eight so a plus seven D. Isn't it? So what do we get? We get five a Plus 20 D is equal to eight a Plus fifty six D. Is it that means if you simplify you'll get eight a minus five a that is three a plus forty thirty six 36 D Is equal to zero Correct, so if you cancel three from you know the equation so you'll get a plus twelve D is equal to zero So a plus twelve D can be written as a plus thirteen minus one D is zero and what is this guys? You all know this is nothing but Thirteenth term thirteenth term is zero and that is what we needed to prove Okay