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  • Find the number of terms in an arithmetic progression with the first term being 3 and the last term being 67, given that the n=10, a=2 common difference is 4.Opt

Find the number of terms in an arithmetic progression with the first term being 3 and the last term being 67, given that the n=10, a=2 common difference is 4.

Option: 1

22


Option: 2

__


Option: 3

__


Option: 4

__


Answers (1)

best_answer

Sixth term $=a+5 d=19$ --------(1)
Twelfth term$=a+11 d=37$ -------(2)
Subtracting equation (1) from equation (2),$6 d=18 \Rightarrow d=3$.
Substituting d=3in equation (1) or (2),$a=4$.
The last term, if the A.P. has n terms, is
$\begin{aligned} & a+(n-1) d \\ & =4+(n-1) 3=67 \\ & \Rightarrow n-1=21 \\ & \Rightarrow n=22 .\end{aligned}$
Hence there are 22 terms in the A.P.


 

Posted by

Ritika Jonwal

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