Question

The first term of a parallel series

Answer 1

$\tt \blue{the \: first \: term \: of \: a \: parallel \: serie s \: is \: \green{ \underline{a}}}$

Hope its help you..

Answer 2

Step-by-step explanation:

First term = 5 .

Step-by-step explanation:

We are given that the first terms of the two parallel series are equal and the ratio of common differences is 1 : 2.

Let the first term of both AP series be a and the common difference of first AP series be and that of second AP series be .

Also, it is given that 7th term of first A.P is 23 and 21th term of second A.P is 125 which means;   = 23    and   = 125

 ⇒  a + (7 - 1)* = 23                 and           a + (21 - 1)* = 125

 ⇒  a + 6* = 23                       and            a + 20* = 125

 ⇒  a = 23 - 6* ---[Equation 1]      and            a = 125 - 20* -----[Equation 2]

Equating both equations we get,

         ⇒  23 - 6* = 125 - 20*

         ⇒  20* - 6* = 102

         ⇒    {by dividing whole equation by }

         ⇒  20 - 6 * =   {because ratio of common differences is 1:2}

         ⇒   = 6

So, putting this value of in equation 2 we get ;

                a = 125 - 20 * 6 = 5

Hence, first term = 5.