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OSWAAL CBSE Sample Question Papers, MAl12426 Find the middle terms of the sequence formed by all numbers between 9 and 95, whichremainder 1 when divided by 3. Also, find the sum of the numbers on both sides of theseparatelyrimMaand nf circle with centre O. At B, a tangent PB is drawn such ththe cherd AB is 16 cm, find its distance from the centre.at its length is 24 cm. The

Answer»

The sequence are formed by all the numbers between 9 and 95 , which leaves remainder 1 when it is divided by 3 : 10, 13, 16, .........94 Here you can see 10, 13 , 16 , .....94 are in AP where first term , a = 10 and common difference , d = 94 . From AP nth term formula , Tn = a + (n -1)d 94 = 10 + (n -1)3 84/3 = n -1 ⇒n = 29

Hence, there are 29 terms between 10 and 94 It means middle term is (n + 1)/2 th term e.g., middle term = (29+1)/2 = 15th term So, T₁₅ = a + (15 - 1)d = 10 + 14 ×3 = 52 Hence, 15th term is 52

here middle is 15th , it means 14 terms are in left side of it and 14 terms are in right side of it. So, sum of first 14 term {left side } = 14/2 [ 2 × 10 + (14 -1)×3 ] [∵Sn = n/2[2a + (n-1)d]= 7[20 + 39] = 7 × 59 = 413

Now, sum of last 14 term { right side of middle term } = S₂₉ -[ S₁₄ + T₁₅ ]= 29/2[2 × 10 + (29-1) × 3 ] - 413 - 52 = 29/2[20 + 84 ] - 465 = 1508 - 465 = 1043


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