Question

29) Find the 31s term of an A.P., whose 11th term is 88 and 16th term is 73. Which
term of this series will be the 1st negative term?​

Answer 1

$\textbf{Formula used:}$

$\text{The n th term of A.P a, a+d, a+2d,........is}$

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

$\textbf{Given:}$

$t_{11}=88\implies\,a+10d=88$ .....(1)

$t_{16}=3\implies\,a+15d=73$ ......(2)

$\text{Subtract (1) from (2), we get}$

$5d=-15$

$\implies\boxed{\bf\,d=-3}$

$\text{(1)}\implies\;a-30=88$

$\implies\boxed{\bf\;a=118}$

$\text{Now,}$

$t_{31}=a+30d$

$t_{31}=118+30(-3)$

$t_{31}=118-90$

$\implies\boxed{\bf\,t_{31}=28}$

$\text{Let t_n be the first negative term}$

$\implies\,t_n<0$

$\implies\,a+(n-1)d<0$

$\implies\,118+(n-1)(-3)<0$

$\implies\,(n-1)(-3)<-118$

$\implies\,(n-1)(3)>118$

$\implies\,n-1>39.1$

$\implies\,n>40.1$

$\text{The integer just greater than 40.1 is 41}$

$t_{41}=a+40d=118-120=-2$

$\therefore\textbf{The first negative term is \bf\,t_{41}=-2 }$

Find more:

1.The 7th and 17th term of an arithmetic progression are 33 and 83 respectively find the ap

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2.If 8 times the 8th term of an AP is equal to 15 times its 15th term then find the 23rd term.

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Answer 2

Answer:

-2

Step-by-step explanation:

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