Question

the 10th term of an ap is 25 and the 18th term is 41 find the 14th term of this ap.​

Answer 1

Answer:

the 10th term of an ap is 25 and the 18th term is 41 find the 14th term of this ap.

Step-by-step explanation:

ANS:→→→→→→→→

Given,

The 10th term of an AP is 25

So, 25=a+9d --------------(1)

And 18th term of an AP is 41

So,41=a+17d ---------------(2)

Let ,by elimination method equation (1)-(2)

a+9d=25

a+17d=41

_______________

-8d=-16d

=>d=-16d/-8d

So d=2

Now,Put value of d put into equation (1)

a+9×2=25

=>a=25-18=7

so we have found value of a=7

So,Now 14th term of this AP is

→→ a+13d

7+13×2

----»»7+26

=>33

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Answer 2

Answer:

ans. 33

Explanation:

t10 = 25 & t18 =41

we know that tn = a+(n-1)×d

:. t10 = a + (10-1) ×d

25 = a + 9d...... (i)

Similarly t18 = a+ (18-1)×d

41 = a +17d

25 = a + 9d

a = 25 -9d

Substituting this value in eq (ii)

a + 17d = 41

.: 25 - 9d + 17d = 41

8d = 41 - 25

8d = 16

.: d = 2

Substituting d = 2 in eq. (i)

a + 9d = 25

a + 9×2 =25

a + 18 = 25

a = 25 - 18

a = 7

Now, tn = a + (n-1) × d

t14 = 7 + (14-1) × 2

t14 = 7 + 13 × 2

t14 = 7 + 26

t14 = 33 ans.

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