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Find the 20th term from the last term of the ap:3, 8,13.........,253 |
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Answer» Given AP is 3,8,13........253 first term a=3 an=253 common difference =5According to Question Let d=-5 a=253 an=3 n=20a+(n-1)d =an =>253 +(n-1)-5 =3=>(n-1)-5=-230 =>(n-1)=-250 /-5=>n-1=50=>n=50+1=>n=51 Given series is 3, 8, 13, ...... 253here, first term , a = 3common difference , d = 5Let us find total number of terms at first.use\xa0=> 253 = 3 + (n - 1)5=> 250 = 5(n - 1)=> n - 1 = 50=> n = 51so, there are 51 terms in given series.now we know, mth term from last =last term - mth term + 1so, 20th term from last = 51 - 20 + 1 = 32hence, 20th from last = 32th term from firstuse ,\xa0T32= a+(32 -1)d= 3 + 31 × 5 = 3 + 155 = 158hence , 20th term from last = 158\xa0 |
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