Question

If the 6th term of an A. P is equal to four times it's first term and the sum of 1st six terms is 75.Find the 1st term and the common difference​

Answer 1

Answer is given in the pic.

Answer 2

Answer:

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a = 5 ; d = 3

Step by step explanation :

Given :

6th term = 4 × 1st term ; S6 = 75

6th term = a+5d ; 1st term = a

According to the question ...

=> a+5d = 4×a

=> a+5d = 4a

=> 5d = 4a - a

=> d = $\frac {3a}{5}$

Formula to be used :

$\huge{\boxed{Sn = {\frac{n}{2}}[2a+(n-1)d]}}$

=>$S6 = {\frac {6}{2}}[2a+(6-1){\frac{3a}{5}}]$

=> $75 = 3[2a+5×{\frac{3a}{5}}]$

=> 75 = 3 [2a+3a]

=> 75 = 15 a

=>${\frac{75}{15}}=a$

=>${\boxed{ a = 5}}$

On Substituting a in d = $\frac{<em>3a</em><em> </em>}{<em>5</em><em> </em>}$

=> ${d = {\frac{3×5}{5}}}$

=> ${\boxed{d=3}}$

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Hope it helps u ............

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