Question

the nth term of an arithmetic progression is an = 4n+5 then the 3rd term is​

Answer 1

$\huge\tt\underline\purple{given✔}$

an-4n+5

to find - 3 rd term ?

SolUtIoN

ap is

let n-1

4n+5

4*1+5

4+5

=9

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

let n-2

4*2+5

8+5

=13

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, , ,,,,,,,

let n-3

4*3+5

=17

ap is 9,13,17 ,,,,,,,,,,,

hence third term is 17

verifying

an=a+(n-1)d

17=9+(n-1)4

17-9=(n-1)4.

8=(n-1)4

2=(n-1)

2+1=n

3=n

$\huge\tt\underline\pink{☁⭐Thanks⭐☁}$

hope its helpful

Answer 2

Question :- The nth term of an arithmetic progression is an=4n+5 then the 3rd term is ?

Solution :-

we know that,

• nth term of an AP = a + (n - 1)d
• a = first term .
• d = common difference .

so,

→ a + (n - 1)d = 4n + 5

→ a + (n - 1)d = 4n - 4 + 4 + 5

→ a + (n - 1)d = 9 + 4n - 4

→ a + (n - 1)d = 9 + (n - 1)4

comparing we get,

• a = 9
• d = 4

therefore,

→ a3 = a + (3 - 1)d

→ a3 = 9 + 2*4

→ a3 = 9 + 8

→ a3 = 17 (Ans.)

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