Question

the 7th term and 17th term of an a.p. is 24 and 54 find 12th term

Answer 1

Gɪᴠᴇɴ:–

In A.P,

7th term is 24

17th term is 54

Tᴏ Fɪɴᴅ :–

12th term of A.P

Sᴏʟᴜᴛɪᴏɴ:–

To, find the 12th term of A.P we need the common difference and first term of A.P.So, Through our data we can find them

tₙ = a + (n-1) d

where,

a= first term

n = term number

d = common difference

So,

7 th term is 24

t₇ = 24

n = 7

Substituting the values,

➳t₇ = a +(7-1) d

➳ 24= a + 6d --- eq❶

17th term is 54

t₁₇ = 54

n = 17

➳ t₁₇ = a+(17-1) d

➳ 54= a + 16d --- eq❷

Now, Subtracting eq1 - eq2

➳24-54 = a+ 6d -(a+16d)

➳-30 = a +6d -a -16d

➳ -30 = -10d

➳ 30 = 10d

➳ d = 30/10

➳ d = 3

So, common difference is 3

Substituting d value in eq 1

➳24 = a + 6d

➳24 = a +6(3)

➳24-18 = a

➳ a = 6

So, the first term is 6.

We need 12th term i.e t₁₂

Substituting the values in formula.

n = 12

a = 6

d = 3

➳t₁₂ = a + (n-1) d

➳t₁₂ = 6 + (12-1) 3

➳t₁₂ = 6 + 11(3)

➳t₁₂ = 6 + 33

➳t₁₂ = 39

So, 12th term of A.P is 39 [tex][/tex]

Answer 2

Answer:

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