The sum of first m terms of an AP is $4 m^{2} - m$ . If the $n^{t h}$ term is $107,$ find the value of $n$ .Also find the $21^{s t}$ term of this AP.

Open in App

Solution

$s u m o f m t e r m s = 4 m^{2} - m t h e n S_{1} = a_{1} = 4 \cdot 1^{2} = 3 S_{2} = a_{1} + a_{2} = 4 \cdot 2^{2} - 2 = 14$
$∴ a_{2} = 14 - 3 = 11 a n d a_{1} = 14 - a_{2} = 14 - 11 = 3 ∴ f i r s t t e r m = 3 a n d c o m m o n d i f f = 8$
$n o w n^{t h} t e r m i s 107 a + (n - 1) d = 107 3 + (n - 1) \cdot 8 = 107 (n - 1) \cdot 8 = 104 n - 1 = (\frac{104}{8}) = 19$
$∴ n = 14$
$n o w a_{21} = a + 20 d$
=3+(20 X 8)
$= 3 + 160 = 163$

Suggest Corrections

Similar questions

The sum of first m terms of an A.P. is $4 m^{2}$ -m. If its nth terms is 107, find the value of n. Also, find the 21st term of this A.P.

(4 n + 1)

15

Join BYJU'S Learning Program