Q. 114.3( 3 Votes )
How many terms of A.P -10, -7, -4, -1, ........ must be added to get the sum 104?
Answer :
Given:
-10, -7, -4, -1, ........
Clearly,
a = -10, d = 3
⇒ 2 × 104 = n[-20 + 3n – 3]
⇒ 208 = n (3n – 23)
⇒ 3n 2 – 23n - 208 = 0
⇒ 3n 2 – 39n + 16n - 208 = 0
⇒ 3n (n – 13) + 16 (n – 13) = 0
⇒ (n – 13) (3n + 16) = 0
⇒ n = 13, 
∵ it cannot be a fraction
∴ n = 13
Hence 13 terms must be added to get the sum of the A.P 104.
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