Question

The sum of first q terms of an A.P. is 63q – 3q². If its pth term is-60, find the value of p. Also, find the 11th term of this A.P.

Answer 1

$\textbf{Given:}$

$S_q=63q-3q^2$

$\text{For q=1,}\;S_1=63-3=60$

$\implies\bf\;a=60$

$\text{For q=2,}\;S_2=126-12=114$

$\implies\;a+(a+d)=114$

$\implies\;2a+d=114$

$\implies\;2(60)+d=114$

$\implies\;d=114-120$

$\implies\bf\;d=-6$

$\text{Also, }t_p=-60$

$\implies\;a+(p-1)d=-60$

$\implies\;60+(p-1)(-6)=-60$

$\implies\;(p-1)(-6)=-120$

$\implies\;p-1=20$

$\implies\bf\;p=21$

$\text{Now,}$

$\bf\;t_{n}=a+(n-1)d$

$t_{11}=a+10d$

$t_{11}=60+10(-6)$

$\implies\boxed{\bf\;t_{11}=0}$

Find more:

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.

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