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Algebra
Question

(a) The first term of an AP is \( a = 7 \) and the...

(a) The first term of an AP is \( a = 7 \) and the fourth term is \( T _ { 4 } = 16 \) . Use the formula 

\( T _ { n } = a + ( n - 1 ) d \) to find the common difference \( d \) . Then write down the first four terms. (b) The first term of an AP is \( a = 100 \) and the sixth term is \( T _ { 6 } = 10 \) . Find the common difference \( d \) using the formula \( T _ { n } = a + ( n - 1 ) d \) . Then write down the next four terms. (c) Find the \( 20 \) th term of an AP with first term \( 28 \) and \( 11 \) th term \( 108 \) . (d) Find the \( 100 \) th term of an AP with first term \( 32 \) and \( 20 \) th term \( - 6 \) . 

Answer

15(a) \( d = 3 ; 7,10,13,16 \quad \) (b) \( d = - 18 ; 82,64,46\) 

\(28 \quad \) (c) \( d = 8 ; T _ { 20 } = 180 \quad \) (d) \( d = - 2 ; T _ { 100 } = - 166\) 

Solution
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