Question

5th and 9th terms of an ap are - 7 and -19 respectively then find first term and common difference of it​

Answer 1

Answer:

The common difference is 3.

Answer 2

${\underline{\underline{\huge{\red{\mathfrak{AnSwEr :}}}}}}$

Given :

• 5 th term is - 7
• 9 th term is - 19

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To Find :

• First term (a) and Common Difference (d)

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Solution :

Use formula

$\LARGE {\boxed{\boxed{\sf{a_n \: = \: a \: + \: (n \: - \: 1)d}}}}$

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✯ Case 1

• Put n = 5

$\implies {\sf{a_5 \: = \: a \: + \: (5 \: - \: 1)d}} \\ \\ \implies {\sf{-7 \: = \: a \: + \: 4d}}---(1)$

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✯ Case 2

• Put n = 9

$\implies {\sf{a_9 \: = \: a \: + \: (9 \: - \: 1)}} \\ \\ \implies {\sf{-19 \: = \: a \: + \: 8d}}----(2)$

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Subtract (1) from (2)

⇒-19 - (-7) = a + 8d - a - 4d

⇒-19 + 7 = 4d

⇒-12 = 4d

⇒d = -12/4

⇒d = -3

$\therefore$ Common Difference is -3

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Now, put value of d in (1)

⇒-7 = a + 4d

⇒-7 = a + 4(-3)

⇒-7 = a - 12

⇒a = -7 + 12

⇒a = 5

$\therefore$ First term is 5