CA Foundation · Quantitative Aptitude · Sequence and Series
How many terms of the AP 54, 51, 48, ... must be added to get a sum of 513?
Either 18 or 19 terms give the sum 513. The equation n² - 37n + 342 = 0 has roots 18 and 19, because the 19th term of the AP is zero, so adding it does not change the sum.
- AOnly 18
- BOnly 19
- CEither 18 or 19Correct
- DOnly 20
Explanation
Sn = n/2[108 + (n-1)(-3)] = n(111 - 3n)/2 = 513, so 3n² - 111n + 1026 = 0, i.e. n² - 37n + 342 = 0. Roots are n = 18 and n = 19. The 19th term is 54 - 54 = 0, so both counts give 513. Choosing only one root ignores that the 19th term is zero.
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