If 36, p,\(\frac{9}{4}\) and q are consecutive terms of an exponential sequence (G.P), find the sum of p and q.
- 9/16
- 81/16
- 9
-
9 \(\frac{9}{16}\)
The correct answer is: D
Explanation
GP : 36, P, \(\frac{q}{4}\), q, ... p + q = ?
| Recall, | common | ratio, | r | = | Tn
Tn-1 |
= | T2
T1 |
= | T3
T2 |
= | T4
T3 |
| ∴ | P
36 |
= | 9
4 |
÷ | p | ; | p\(^2\) | = | 9
4 |
x | 36 | ; | p\(^2\) | = | 81 |
| p | = | 9 | ∴ | r | = | T2
T1 |
= | 9
36 |
= | 1
4 |
| Also | r | = | T4
T3 |
= | q | ÷ | 9
4 |
∴ \(\frac{1}{4}\) = q ÷ \(\frac{9}{4}\) ;
\(\frac{9}{4}\) = 4q
| 16q | = | 9 | , | q | = | 9
16 |
∴ | p | + | q | = | 9 | + | 9
16 |
= | 9 | 9
16 |