Question

The sum of first m terms of an A.P. is 4 m² - m. If its nth term is 107, find the value of n. Also, find the 21st term of this A.P.

Answer 1

$\textbf{Given:}$

$S_m=4m^2-m$

$\text{For m=1,}\;S_1=4-1=3$

$\implies\boxed{\bf\,a=3}$

$\text{For m=2,}\;S_2=16-2=14$

$\implies\,a+(a+d)=14$

$\implies\,6+d=14$

$\implies\boxed{\bf\,d=8}$

$\text{Also,}\;t_n=107$

$\implies\,3+(n-1)8=107$

$\implies\,(n-1)8=104$

$\implies\,n-1=\frac{104}{8}$

$\implies\,n-1=13$

$\implies\boxed{\bf\;n=14}$

$\text{Now,}$

$\bf\,t_n=a+(n-1)d$

$t_{21}=a+20d$

$t_{21}=3+20(8)$

$\implies\boxed{\bf\,t_{21}=163}$

Find more:

In an A.P. if Sn = 3n2 - n and its common difference is ‘6’ then first term is ______

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Answer 2

Answer:

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