Which term of the AP 18, 15.5, 13….-47?

an important question from the book -ML aggarwal( avichal publication)class 10th , chapter9, arithmetic progression …….. This type of question has been asked in paper. so please solve it in detail. we have been asked

Which term of the AP 3, 8, 13, 18 is 78?

Clasa 10, ML Publication, Arithmetic Progression Chapter 3 question no. 6(iii)

Rajan@2021Guru

# Which term of the AP 18, 15.5, 13….-47?

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## Given sequence is 18,1521,13,...,−47

The first term a=18 and

the common difference d=1521−18=−2.5

the last term is −47

Let the last term be the nth term

We know that the nth term of the arithmetic progression is given by a+(n−1)d

Therefore, a+(n−1)d=−47

⟹18+(n−1)∗(−2.5)=−47

⟹18+2.5−2.5n=−47

⟹20.5−2.5n=−47

⟹2.5n=20.5+47

⟹n=67.5/2.5

⟹n=27

Therefore, the number of terms in the given sequence is 27