Question

The 9th term of an AP is -32 and the sum of its 11th term and 13th term is -94. Find common difference if 4 times the 4th term of an AP is equal to 18 times its 18th term . Find its 22nd term

Answer 1

T9 = - 32
a+8d = - 32 -------(1)

T11+T13 = - 94
=> a+10d +a +12d = - 94
=> 2a + 22 d = - 94
=> a+11d = -47 -----(2)

(1)-(2),we get
-3d = 15
=> d = - 5

a=8

T22 = a+21d
= 8 + 21 (-5)
= 8 - 105
= - 97

Answer 2

We are given, a9 = -32
                       a + 8d = -32   ...................................(1)

 We are also given, a11+a13 = -94
                     = a + 10d + a +12d = -94
                       2a + 22d = -94 
                    = a + 11d = -47 ...................................(2)

 By Subtracting Eqn (2) from Eqn (1)

                  a + 8d = -32
                +a + 11d = -47 
               -     -            +
                     -3d = 15
               so, d = -5

      By Putting d = -5 in Eqn (1)

      a + 8(-5) = -32
      a = -32 + 40 
     a = 8 
                          
so ,a22 = a + 21d = 8 + 21(-5)
            = 8 -105
            = -97

Hence 22th term is -97
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