PRC-2 · Chapter 3 · Question 18 of 45
In an arithmetic progression, the first term is 12 and the common difference is 4. How many specific terms are needed to produce a total sum of exactly 320?
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: B) 10
Explanation
Using the formula Sn = (n/2)[2a + (n-1)d]: 320 = (n/2)[24 + (n-1)4]. This expands to 640 = n(20 + 4n) -> 4n^2 + 20n - 640 = 0 -> n^2 + 5n - 160 = 0. Factoring yields (n-10)(n+16)=0. Thus, n=10.
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