Question

In the AP : 29, 27, ..., 5 (i) the number of terms is (a) 24 (b) 11 (c) 13 (d) 15 (ii) The sum of these terms is (a) 408 (b) 221 (c) 187 (d) 255​

Answer 1

Answer:

number of terms = 13

sum of these terms = 221

Step-by-step explanation:

AP : 29, 27,..., 5

a = 29 , d = ( -2 )              [ a is the first term and d is the common difference ]

$a_{n}$ = 5                               [ nth term \ the last term ]

$a_{n}$ = a + (n - 1) * d         [ n is the number of terms ]

5 = 29 - (n - 1) * 2             [ sign got changed as d was negative ]

 5 - 29 = - 2n + 2

- 26 = - 2n

n = 13

total numbers of terms is 13

s₁₃ = (n/2) * ( 2a + (n - 1) * d )                [ s₁₃ is the sum of all 13 terms ]

s₁₃ = $\frac{13}{2} (58 - 24)$

s₁₃ = $\frac{13}{2}*34$

s₁₃ = 13 * 17

s₁₃ = 221

sum is 221

Answer 2

(ii) The quadratic equation formed is, , (a) 2x7 - 70x + 600 = 0 (b) 2x? - 70x - 600 = 0, , (c) 2x7 - 70x - 1850 = 0 (d) 2° + 70x - 1850 = 0, (iii) The factor form of the equation is, , (a) (x - 15)(x - 20) = 0 (b) (x - 30)(x - 5) = 0, , (c) (x + 65)(x = 30) = 0 (d) (x - 20)(x - 30) = 0, , (iv) The value of x is, (a) 30 or 20 (b) 30 or 5 (c) 30 or -65 (d) 15 or 20, 25. The nth term of an AP is 3n - 2., (i) The first 3 terms are, , (a) 13,5 (b) 3, 6,9 (147 (d) 3, 5,7, (ii) The common difference is, , (a) 2 (b) 3 (c) -2 (da) -3, (iii) Sum of the first 10 terms of this AP is, , (a) 210 (b) 56 (c) 145 (d) None of these, (iv) Which of the following is not a term of the AP?, , (a) 25 (b) 49 (¢ 45 (d) 31, ,