Question

For A.P sixth term is -10 and fourteenth term is -34 find value of tenth term *​

Answer 1

Given:

a6 = (-10)

a14= (-34)

To Find :

a10 = ?

Answer :

a6=a+(5)d=(-10) ______(1)

a14=a+(13)d=(-34)_____(2)

Solving 1 and 2

$a + 5d = (- 10) \: \: \: \: \: \: \: \\ \underline{a + 13d = ( - 34) } \: ( - ) \\ - 8d = 24 \: \: \: \: \\ \\ d = \frac{ - 24}{8} \\ \bf d = ( - 3)$

$Substituting~d=(-3)~in~(1)$

$a +5 ( - 3) = ( - 10) \\ a - 15 = ( - 10) \\ a = - 10 + 15 \\ \bf{a = 5}$

$\\ \\ a10 = a + 9d \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = (5) + 9( - 3) \\ = 5 - 27 \: \: \: \: \: \: \: \: \: \: \: \\ = \bf- 22 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\\ \\ \\ { \bf{Hope \: \: this \: \: helps \: \: you \: !}}$