Question

the 17th term of an ap is 5 more than twice its 8th term .if the 11th term of an ap is 43 .find the 50th term​

Answer 1

Step-by-step explanation:

the 17th term of an ap is 5 more than twice its 8th term .if the 11th term of an ap is 43 .find the 50th term

Answer 2

✤ Required Answer:

✒ GiveN:

17th term of an AP is 5 more than twice of 8th term.

11th term is 43

✒ To FinD:

Find its 15th term....?

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✤ How to solve?

For the above question, We need to know the formula of nth term of an AP, That is:

\large{ \boxed{ \sf{a_n = a + (n - 1)d}}}

a

n

=a+(n−1)d

Here, an is the last term, a is the first term, n is the no. of terms and d is the common difference. ☃️ So, let's solve this question...

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✤ Solution:

By using the above formula,

a17 = a + 16d

a8 = a + 7d

a11 = a + 10d

According to condition-1)

➝ a17 = 2a8 + 5

➝ a + 16d = 2(a + 7d) + 5

➝ a + 16d = 2a + 14d + 5

➝ a - 2a + 16d - 14d = 5

➝ - a + 2d = 5

➝ - a = 5 - 2d

➝ a = 2d - 5.........(1)

According to condition-2)

➝ a11 = 43

➝ a + 10d = 43

Substituting value of a in this eq.

➝ 2d - 5 + 10d = 43

➝ 12d - 5 = 43

➝ 12d = 48

➝ d = 48/12

➝ d = 4

Putting the value of d in eq.(1),

➝ a = 2(4) - 5

➝ a = 8 - 5

➝ a = 3

We have to find, a15

➝ a15 = a + 14d

➝ a15 = 3 + 14(4)

➝ a15 = 3 + 56

➝ a15 = 59

☀️ 15th term of the AP = 59

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