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Y, (Y + 9), (Y + 18), ....... 20 terms. where Y is the integer root of: 3y2 – 23y + 14 = 0 Find the sum of last 10 terms of series.

Y, (Y + 9), (Y + 18), ....... 20 terms. where Y is the integer root of: 3y2 – 23y + 14 = 0 Find the sum of last 10 terms of series. Correct Answer 1375

3y2 – 23y + 14 = 0

3y2 – 21y – 2y + 14 = 0

3y(y – 7) – 2(y – 7) = 0

y = 7 or 2/3

Hence series will be 7, (7 + 9), (7 + 18) ... 20 terms.

20th term = 7 + 19 × 9 = 178

This series can be considered as an Arithmetic Progression with a = 178 and d = – 9 (since series starts with last term)

S10 = 10/2

S10 = 5 × (356 – 81) = 5 × 275 = 1375

Alternative method:

After finding the value of y = 7

sum of last 10 terms of series = Sum of first 20 term – Sum of first 10 terms

sum of last 10 terms of series = S20 – S10

sum of last 10 terms of series = 1850 – 475 = 1375

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