Question

The 5th term of an AP is 26 and the 10th term is 51.Find the 15th term of the AP​

Answer 1

A+4d=26

A+9d=51

Solving both equations

Substracting 1 from 2

A+9d=51-(A+4d=26)

Reamaining eq

5d=25

So d=5

Now putting value of d in eq 2

A+4*5=26

A=26-20

A=6

Now you can find ap as first term and common difference is there

Answer 2

a5=a+4d=26

a+4d=26..........(1)

a10=a+9d=51

a+9d=51.............(2)

a+4d=26

a+9d=51

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-5d=-45

cancel all minus

5d=45

d=9..........(3)

substitute (3) in (1)

a+4d=26

a+4(9)=26

a+36=26

a=-10

15th term is a15

a15=a+14d

a+14d=-10+14(9)

-10+126

-116

so, 15th term is -116