Let-a-1-a-2-a-10-be-in-AP-and-h-1-h-2-h-10-be-in-HP-If-a-1-h-1-2-and-a-10-h-10-3-then-a-4-h-7-is-

Question Number 56421 by gunawan last updated on 16/Mar/19

Let a_{1}, a_{2}, \dots, a_{10} be in AP and h_{1}, h_{2}, \dots, h_{10}

be in HP . If a_{1} = h_{1} = 2 and a_{10} = h_{10} = 3,

then a_{4} h_{7} is

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19

a_{1} = 2 \to a_{10} = a_{1} + 9 d \to

3 = 2 + 9 d \to d = \frac{1}{9}

a_{4} = a_{1} + 3 d \to 2 + \frac{3}{9} \to \frac{7}{3}

\frac{1}{h_{10}} = \frac{1}{h_{1}} + 9 d_{1} \to \frac{1}{3} = \frac{1}{2} + 9 d_{1}

\frac{1}{3} - \frac{1}{2} = 9 d_{1}

d_{1} = \frac{- 1}{54}

\frac{1}{h_{7}} = \frac{1}{h_{1}} + 6 \times d_{1} \to \frac{1}{h_{7}} = \frac{1}{2} - \frac{6}{54} \to \frac{27 - 6}{54} = \frac{21}{54}

a_{4} h_{7} \to \frac{7}{3} \times \frac{54}{21} \to 6