Question

in an AP,if a=3,n=8,Sn=192,find d​

Answer 1

${\huge{\underline{\underline{\bf{Answer}}}}}$

★ In this Progression ,

$\bf{a \: (first \: term) = 3}$

$\bf{n(number \: of \: terms) = 8}$

$\bf{sn(sum \: of \: n \: terms) = 192}$

Now , using the Formula for Sn

$sn \: = \frac{n}{2} (2a + (n - 1)d)$

Now , Substitute the values..

$\implies \red{192} \: = \frac{8}{2} (2 \times 3 + 7 \purple d)$

$\implies \: \pink{ 192} = 4(6 + 7 \green d)$

$\implies \: 48 = 6 + 7 \blue{d}$

$\implies \: 42 = 7 \red{d}$

$\implies \: \boxed{ \green d = 6}$