Question

The 7 th term of an A.P is -1 and it's 16 thterm is 17. The n th term of the A .P is​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• 7th term of AP is -1.

• 16th term of AP is 17.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• 'n'th term of AP.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

$\bigstar \boxed{ \bf \: a_{n} = a + (n - 1)d}$

Here ,

• a(n) 'n'th term

• a 1st term

• n is number of terms

• d common difference

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➽ 7th term of AP is -1.

➛ -1 = a + (7-1)d

➛ -1 = a + 6d ㅤㅤㅤㅤ-------(i)

➽ 16th term is 17

➛ 17 = a + (16-1)d

➛ 17 = a + 15d ㅤㅤㅤ-------(ii)

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Subtracting eqⁿ (i) from eqⁿ (ii)

➛ 17 - (-1) = a + 15d - ( a + 6d )

➛ 17 + 1 = a + 15d - a - 6d

➛ 18 = 9d

➛ d = 18/9

➛ d = 2

➣ Putting d = 2 in eqⁿ (i)

➛ -1 = a + 6d

➛ -1 = a + 6(2)

➛ -1 = a + 12

➛ a = -1-12

➛ a = -13

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'n'th term , a(n) = a + (n-1)d

➣ Putting values ,

➛ a(n) = -13 + (n-1)2

➛ a(n) = -13 + 2n - 2

➛ a(n) = -15 + 2n

Hence , nth term is (-15+2n).