Question

The largest positive term of H.P. whose first two terms are $\frac{2}{5}$ and $\frac{12}{23}$ is

• A. 2
• B. 6
• C. 12
• D. 20

Answer 1

Answer: (B)

6

Answer 2

A.P. is $\frac{5}{2},\frac{23}{12}$,……..

T_n = $\frac{5}{2}$ + (n – 1) $\left( \frac{23}{12} - \frac{30}{12} \right)$

T_n = $\frac{5}{2} - \frac{7(n - 1)}{12}$ > 0

Ž 30 > 7(n – 1)

Ž n – 1 < $\frac{30}{7}$

Ž n < $\frac{37}{7}$

so n = 5

so largest term

T_n = $\frac{5}{2} - \frac{7.4}{12}$ = $\frac{5}{2} - \frac{7}{3}$ = $\frac{1}{6}$

for H.P. = 6