Question

if 21, a, b, -3 are in AP, find the value of a and b

Answer 1

$\huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \bold{a=13, \ \ b=5}\ \ \ \ \ }\ \ \ \ \ }\ \ \ \ \ }$

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$T_1=21 \\ \\ T_2 = a \\ \\ T_3 = b \\ \\ T_4 = -3$

$T_4 - T_1 = -3-21 \\ \\ (4-1)d=-24 \\ \\ 3d=-24 \\ \\ d=-8$

$T_2-T_1=(2-1)d \\ \\ a-21=1 \times -8 \\ \\ a-21=-8 \\ \\ a=-8+21 \\ \\ a=\bold{13}$

$T_4-T_3=(4-3)d \\ \\ -3-b=1 \times -8 \\ \\ -3-b=-8 \\ \\ b=-3+8 \\ \\ b=\bold{5}$

$\therefore\ 21,\ 13,\ 5,\ -3,...\ \ is the AP. \\ \\ \\ Hope it helps. Please mark it as the brainliest. \\ \\ \\ Thank you. :-)$