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4. How many terms are there in the A.P.?
Arithmetic Progression | Class 10 | ICSE | Maths | RD Sharma
4. How many terms are there in the A.P.?

(iii) 7,13,19, …,205

(iv) 18,15{\scriptstyle{}^{1}/{}_{2}},13, ….,-47

An arithmetic progression or arithmetic sequence is a number’s sequence such that the difference between the consecutive terms is constant.

Solutions:

(iii) Given, A.P. 7,13,19, …, 205

Here, a=7 and d={{a}_{2}}-{{a}_{1}}=13-7=6

We know that, {{n}^{th}} term {{a}_{n}}=a+\left( n-1 \right)d

And, given {{n}^{th}} term {{a}_{n}}=205

a+\left( n-1 \right)d=205

7+\left( n-1 \right)\left( 6 \right)=205

7+6n-6=205

6n=205-1

n=204/6

⇒ n=34

Therefore, there are 34 terms in the given A.P.

(iv) Given, A.P. 18,15{\scriptstyle{}^{1}/{}_{2}},13, …., -47

Here, a=7 and d={{a}_{2}}-{{a}_{1}}=15{\scriptstyle{}^{1}/{}_{2}}-18=5/2

We know that, {{n}^{th}} term {{a}_{n}}=a+\left( n-1 \right)d

And, given {{n}^{th}} term {{a}_{n}}=-47

a+\left( n-1 \right)d=43

18+\left( n-1 \right)\left( -5/2 \right)=-47

18-5n/2+5/2=-47

36-5n+5=-94

5n=94+36+5

5n=135

⇒ n=27

Therefore, there are 27 terms in the given A.P.

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