Question

6th term of ap is -10 and 10th term is -26 determine 15th term of ap

Answer 1

Answer:

-46

Step-by-step explanation:

we can write 6th term as A+5D=-10(1) AND 10th term as A=9D=-26.(2)

NOW SUBTRACT THE BOTH EQUATIONS:-

A+5D=-10-(1)

A+9D=-26-(2)

so,-4D=16 hence d=-4

A+5(-4)=-10

A-20=-10

A=-10+20

∴A=10

∴SO, WE CAN WRITE 15TH TERM AS A+14D=10+14(-4)=10-56=-46

hence the value of the 15th term is -46

HOPE IT WILL HELP YOU

Answer 2

$\bf\large\underline\green{Solution:-}$

$\sf{{a_n} = a+ (n - 1)d}$

$\sf{{a_6} = a+ (6 - 1)d \:and\: a - 10 = a +(10 - 1) d}$

$\sf{{a_6} = a + 5d \: \:and \: \:{a}_{10}= a + 9d}$

=> a + 5d = -10 ⠀⠀⠀⠀ ................(i)

=> a + 9d = -26 ⠀⠀⠀⠀ .................(ii)

On subtracting (i) from (i), we get

=> 4d = -16

=> d = -4

On substituting d= -4 in (i), we get

=> a + 5 x (-4) - 10

=> a = 10

Thus, a = 10 and d = -4

$\sf{15^{th}\: \:term = {a}_{15} = a + (15 - 1) d}$

$\sf{=\:(a + 14d) = [10 +14\:x\:(-4)]}$

$\sf{= (10 - 56)}$

$\sf\boxed{\red{\underline{= -46}}}$