Question

Q) The 5th term of an arithmetic sequence is 38 and 9th term is 66.
what is its 25th term.
Answer this question with step by step explanation.​

Answer 1

$\huge\underline\bold\purple{★ QUESTION :}$

The 5th term of an arithmetic sequence is 38 and 9th term is 66.What is its 25th term.

$\huge\underline\bold\purple{★ SOLUTION :}$

Given that,

• a5 = 38
• a9 = 66

We can write these terms as...

• a5 → a + 4d = 38...... (1)
• a9 → a + 8d = 66...... (2)

Now, subtract the equations (1) & (2), we get

➡ - 4d = - 28

➡ 4d = 28

➡ d = 7

$\boxed{∴ d = 7 }$

Now, substitute the value of d in (1)

➡ a + 4(7) = 38

➡ a + 28 = 38

➡ a = 38 - 28

➡ a = 10

$\boxed{∴ a = 10 }$

To find the value of 25th term,

↪ an = a + (n - 1)d

• a = 10
• d = 7
• n = 25

➡ a25 = 10 + (25 - 1)(7)

➡ a25 = 10 + 24(7)

➡ a25 = 10 + 168

➡ a25 = 178

$\boxed{∴ The\;value\;of\;25th\;term\;is\;“178” }$

Step-by-step explanation:

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