Question

the 20th term of an arithmetic sequence is 60 and 16th term is 20 .find the first term and the common difference

Answer 1

$\huge{\bold{\underline{\underline{Question:-}}}}$

The 20th term of an arithmetic sequence is 60 and 16th term is 20 .find the first term and the common difference.

$\huge{\bold{\underline{\underline{Solution:-}}}}$

a20 = 60

a16 = 20

Now,

a20 = a+19d = 60 ............(1)

a16 = a+15d = 20 ...............(2)

Subtracting (2) from (1)

a + 19d = 60 .......(1)

a + 15d = 20 .......(2)

_ _ _

—————————————

4d = 40

d = 40/4

$\large{\purple{\boxed{\orange{d \:=\: 10}}}}$

Now, putting the value of 'd' is (1)

a + 19d = 60

a + 19(10) = 60

a + 190 = 60

a = 60-190

$\large{\purple{\boxed{\orange{a \:=\: -130}}}}$

∴ Value of a = (-130) and d = 10 .......

Verification :-

a = (-130)

d = 10

a20 = a + 19d

= (-130) + 19*10

= (-130) + 190

= 60

a16 = a + 15d

= (-130) + 15*10

= (-130) + 150

= 20