Question

if 20th term and 30th term of Arthematic progression are 121 and 181 respectively find the 40th term of Arthematic progression​

Answer 1

Answer:

$\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}$

✬ 40th Term = 241 ✬

Step-by-step explanation:

Given:

20th and 30th term of an AP is 121 and 181 respectively.

To Find:

What is the 40th term of AP ?

Solution: As we know that an AP series is given by

★ a + (n – 1)d ★

• a = first term
• n = number of terms
• d = common difference

A/q

20th term is 121.

➙ a + (20 – 1)d = 121

➙ a + 19d = 121

➙ a = 121 – 19dㅤㅤㅤㅤㅤeqⁿ i

Now ,

30th term is 181

➙ a + (30 – 1)d = 181

➙ a + 29d = 181

➙ 121 – 19d + 29d = 181 ㅤㅤㅤfrom eqⁿ i

➙ 10d = 181 – 121

➙ d = 60/10 = 6

So the common difference of AP is 6. Now putting the value of d in eqⁿ 1.

➮ a = 121 – 19 × 6

➮ a = 121 – 114

➮ a = 7

So the first term of AP is 7.

∴ 40th term will be

⟹ a + (40 – 1)d

⟹ 7 + 39 × 6

⟹ 7 + 234

⟹ 241

Hence, the 40th term of AP will be 241.

Answer 2

Answer:

241 Answer

Step-by-step explanation:

$a_{20} = 121\\a_{30} = 181\\a_{40} = ?$

$a_{20} = 121\\a + (20 - 1) * d = 121\\a + 19d = 121 ------equation 1\\a_{30} = 181\\a + (30-1) * d = 181\\a + 29d = 181 ----------equation 2\\Subtracting equation 2 from 1\\29d - 19d = 181 - 121\\10d = 60\\d = 6$

Putting value of d in equation 1

a + 19(6) = 121

a + 114 = 121

a = 121-114

a = 7

Now, a40 = a + (40-1) X d

= 7 + 39(6)

= 7 + 234

= 241 Answer