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(a) Which term of the progression 4 + 8 ...

(a) Which term of the progression 4 + 8 + 12 + ... is 76 ?
(b) Which term of the progression 36 + 33 + 30 + ... is zero ?
(c) Which term of the progression `(3)/(4)+1+(5)/(4)+..." is "12?`

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Let's solve the question step by step. ### Part (a): Which term of the progression 4 + 8 + 12 + ... is 76? 1. **Identify the first term and common difference**: - The first term \( a = 4 \) - The common difference \( d = 8 - 4 = 4 \) 2. **Use the formula for the nth term of an arithmetic progression**: - The formula for the nth term \( a_n \) is given by: \[ a_n = a + (n - 1) \cdot d \] - We need to find \( n \) such that \( a_n = 76 \). 3. **Set up the equation**: \[ 76 = 4 + (n - 1) \cdot 4 \] 4. **Simplify the equation**: \[ 76 = 4 + 4n - 4 \] \[ 76 = 4n \] 5. **Solve for \( n \)**: \[ n = \frac{76}{4} = 19 \] Thus, the 19th term of the progression is 76.

Let's solve the question step by step. ### Part (a): Which term of the progression 4 + 8 + 12 + ... is 76? 1. **Identify the first term and common difference**: - The first term \( a = 4 \) - The common difference \( d = 8 - 4 = 4 \) ...
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NAGEEN PRAKASHAN ENGLISH-SEQUENCE AND SERIES-Exercise 9B
  1. (a) The nth term of a progression is (3n + 5). Prove that this progres...

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  2. (a) Find the 10th term of the progression 1 + 3 + 5 +7+ ... (b) Find...

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  3. (a) Which term of the progression 4 + 8 + 12 + ... is 76 ? (b) Which...

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  4. (a) Find the 16th term from the end of the progression 3 + 6 + 9 + ......

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  5. (a) How many numbers of two digits are divisible by 3 ? (b) How man...

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  6. (a) Find the value of 'x if x + 1, 2x + 1 and x + 1 are in A.P. Also f...

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  7. (a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find...

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  8. Given that the (p+1)th term of an A.P. is twice the (q+1)th term, prov...

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  9. The 12th term of an A.P. is 14 more than the 5th term. The sum of thes...

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  10. (a) Is 303, a term of the progression 5, 10, 15, ... ? (b) Is 38, a...

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  11. Prove that the sum of nth term from the beginning and nth term from th...

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  12. In an A.P., prove that : T(m+n) + T(m-n) = 2*T(m)

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  13. (i) 10 times the 10th term and 15 times the 15th term of an A.P. are e...

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  14. Which term of the A.P. (16-6i,)(15-4i), (14-2 i), ... is a : (a) pur...

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  15. (a) Which term of the progression 10,9(1)/(3),8 (2)/(3),...is the firs...

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  16. Each of two arithmetic progressions 2, 4, 6, ... and 3, 6, 9, ... are ...

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  17. If a(1),a(2),….a(n) are in arthimatic progression, where a(i)gt0 for a...

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  18. If the numbers a , b , c , d , e form an A.P. , then find the value of...

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