Question

t7=10 t13=34 find t10​

Answer 1

Given

We have given t₇ = 10 & t₁₃ = 34

To Find

We have to find t₁₀ = ?

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

We have two term given t₇ = 10 & t₁₃ = 34

➙t₇ can be written as : a+6d

➙ t₁₃ can be written as a+12d

Now, a+6d = 10

$\:\:\:\:\:\:\:$a+12d=34

$\:\:\:\:$$(-)(-)\:(-)$

$\:\:\:\:$___________

$\:\:\:\:$-6d= -24

$\:\:\:\:$6d= 24

$\:\:\:\:$d=24÷6=4

Hence,d(common difference ) is 4

Now,put d's value into this equation

➙a+6d=10

➙a+6(4)=10

➙a+24=10

➙a=10-24=-14

a= -14

We have a = -14 & d=4

Now,we havebe to find t₁₀

➙t₁₀ can be written as a+9d

➙a+9d= -14+9(4)

➙-14+36=22

Hence,t₁₀ is 22

Answer 2

Step-by-step explanation:

t7 = 10

t + 6d = 10

t = 10-6d ----(1)

t13 = 34

t + 12d = 34

from eq1

10 - 6d + 12d = 34

6d = 24

d = 4

t = 10 - 24 = -14

t10 = t + 9d

= -14 + 36

=22