Find the common difference and $99^{t h}$ term of the arithmetic progession :

$7 \frac{3}{4}, 9 \frac{1}{2}, 11 \frac{1}{4}, . . . . . . . . . . . .$

Open in App

Solution

$A P : 7 \frac{3}{4}, 9 \frac{1}{2}, 11 \frac{1}{4}, . . . . . . . . . . . o r A P : \frac{31}{4}, \frac{19}{2}, \frac{45}{4}, . . . . . . . . . . . o r A P : \frac{31}{4}, \frac{38}{4}, \frac{45}{4}, . . . . . . . . . . . a = \frac{31}{4} d = a_{2} - a_{1} = \frac{38}{4} - \frac{31}{4} = \frac{38 - 31}{4} = \frac{7}{4}$

$n^{t h} t e r m, a_{n} = a + (n - 1) d = a_{99} = \frac{31}{4} + (99 - 1) \frac{7}{4} = \frac{31}{4} + 98 \times \frac{7}{4} = \frac{31}{4} + \frac{392}{4} = \frac{392 + 31}{4} = \frac{423}{4} = 105 \frac{3}{4}$

Suggest Corrections

Similar questions

99 t h

7 \frac{3}{4}, 9 \frac{1}{2}, 11 \frac{1}{4}, . . . . . . . . . . . .

99 t h

7 \frac{3}{4}, 9 \frac{1}{2}, 11 \frac{1}{4}, \dots \dots \dots \dots \dots \dots

If the $3^{r d}$ and the $9^{t h}$ terms of an arithmetic progession are 4 and -8 respectively, which term of it is zero ?

Find the first term of an arithmetic progression, if its $7^{t h}$ term is 4 and common difference is -4.

4

22

\frac{1}{4}

Join BYJU'S Learning Program