Question

aD
The 5th and 12th team of
asithmetic sequence ale 17 and
38. Find the 23rd team?​

Answer 1

Answer:

let a is the 1st term and b is the common difference

a+4b=17

a+11b=38

subtract ing the two equations

a+11b-a-4b=38-17

7b=21

b=3

a+4×3=17

a=17 -12=5

23rd term is

5+(23-1).3=5+22.3=5+66=71

Answer 2

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✤ Correct Question:

The 5th term and 12th term of the Arithmetic progression is 17 and 38. Then, find the 23rd term?

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✤ Required Answer:

⚡GiveN:

• 5th term = 17
• 12th term = 38

⚡To FinD:

• 23rd term of the AP......?

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✤ How to solve?

The above question can be solved by using the nth term formula of the AP that is given by,

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

Here,

• an = nth term of the AP
• a = first term of the AP
• n = number of terms
• d = common difference

☀️ So, Let's solve this question....

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✤ Solution:

We have,

• 5th term = 17
• 12th term = 38

By using nth term formula,

• a5 = a + 4d = 17
• a12 = a + 11d = 38

Subtracting equation (1) from equation (2),

➝ a12 - a5 = 38 - 17

➝ a + 11d - (a + 4d) = 21

➝ a + 11d - a - 4d = 21

➝ 7d = 21

➝ d = 21/7 = 3

Putting value of d in eq.(1),

➝ a + 4(3) = 17

➝ a + 12 = 17

➝ a = 5

Then, 23rd term,

• a23 = a + 22d

Putting values of a and d,

➝ a23 = 5 + 22(3)

➝ a23 = 5 + 66

➝ a23 = 71

❄ 23rd term of the AP = 71

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