Question

if 8th and 19th term of an A.P are 21 and 43 respectively then find 47th term ?​

Answer 1

Required Answer:-

Given:

• The 8th term of an A.P. is 21.
• The 19th term of an A.P. is 43.

To find:

• The 47th term.

Solution:

We know that,

➡ Nth term of an A.P. = a + (n - 1)d

Here,

➡ 8th term = 21

➡ a + (8 - 1)d = 21

➡ a + 7d = 21 .......(i)

Again,

➡ 19th term = 43

➡ a + (19 - 1)d = 43

➡ a + 18d = 43 .......(ii)

Subtracting (i) from (ii), we get,

➡ a + 18d - a - 7d = 43 - 21

➡ 11d = 22

➡ d = 2

Hence, the common difference is 2.

Substituting d in (i), we get,

➡ a + 7 × 2 = 21

➡ a + 14 = 21

➡ a = 7

Hence, the first term of the A.P. is 7.

So, it's 47th term will be,

= a + (47 - 1)d

= a + 46d

= 7 + 46 × 2

= 7 + 92

= 99

Hence, the 47th term of this A.P. is 99.

Answer:

• The 47th term of the given A.P. is 99.

Answer 2

Answer:

8th term= a+7d=21-------(1)

19 the term = a+18d=43-------(2)

subtracting eq 1&2

a+18d=42

a+7d=21

11d=22

d=2

a+2×7=21

a=21-14

a=7

a+46d

7+46×2

7+92

99

Hope that this will help you