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

Open in App

Solution

Given $S_{m} = (4 m^{2} - m)$

$a_{n} = 107$

$a + (n - 1) d = 107$

$S_{1} = 4 \times 1 - 1 = 3$

$S_{2} = 4 \times 4 - 2 = 14$

$S_{2} - S_{1} = a_{2} = 11$

$a + d = 11.$

[ d=8]

$a = 11 - d = 11 - 8 = 3$

$a + 8 n = 115.$

$3 + 8 n = 115.$

$n = \frac{112}{8} = 14$

$a_{21} = a + 20 d = 3 + 20 \times 8 = 163$

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.

m

4 m^{2} - m

n^{t h}

107

n

Join BYJU'S Learning Program