Question

the 20th and 30th terms of an AP are 201 and 301 respectively. Find c.d
​

Answer 1

here's your answer friend☺☺☺

..

Answer 2

Common difference(d) = 10

Step-by-step explanation:

★ Given that,

➡ 20th term of an AP : 201

• a20 = 201

➡ 30th term of an AP : 301

• a30 = 301

★ To find,

• Common difference(d).

★ Let,

◼ a20 : a + 19d = 201 ..... (1)

◼ a30 : a + 29d = 301 ..... (2)

• Subtract equations (1) & (2)

a + 19d = 201

a + 29d = 301

- - -

_____________

- 10d = - 100

_____________

➠ - 10d = - 100

➠ 10d = 100

➠ d = 100/10

➠ d = 10

Now substitute the value of d in equation (1).

➠ a + 19(10) = 201

➠ a + 190 = 201

➠ a = 201 - 190

➠ a = 11

★ Verification,

Substitute the values of a & d in (1), to get LHS = RHS.

LHS = a + 19d

➠ 11 + 19(10)

➠ 11 + 190

➠ 201

Since, LHS = RHS.

Hence, it was verified.

∴ Common difference (d) = 10

★ More info :

Formula related to Arithmetic Progression :

☯ an = a + (n - 1)d

☯ Sn = n/2[ 2a + (n - 1)d ]

Where,

• a = first term of AP.
• n = number of terms of AP.
• d = common difference(d) of AP.
• an = nth term of AP.
• Sn = sum of nth terms of AP.

______________________________________________________