Question

The number of terms of an AP -10,-7,-4,-1......which makes the sum 104 is: *​

Answer 1

Answer:

The number of terms to form the sum 104 = 13

Step-by-step explanation:

AP is -10,-7,-4,-1......

Therefore,

a = -10

d = -7 - (-10)

= 3

Sum of terms is given as 104

Sn = n/2 [ 2a + (n - 1) d ]

104 = n/2 [ 2 (-10) + (n -1) 3]

104 = n/2 [ -20 + 3n - 3 ]

104 = n/2 [ -23 + 3n ]

208 = -23n + 3n²

or 3n² - 23n - 208 = 0

Solving the equation

n = [-b + or - √b² - 4ac ] ÷ 2a

= [-(-23) + or - √(-23)²-4×3×- 208 ] ÷ 2 × 3

= [23 + or - √529 + 2496 ] ÷ 6

= [23 + or - √3025 ] ÷ 6

= [23 + or - 55 ] ÷ 6

Therefore,

n = (23 + 55) / 6 = 78/6 = 13

or

n = (23 - 55) / 6 = -32/6

Since n cannot be negative, we take the value n = 13