Question

2nd, 31st and the last term of an A.P. are 31/4, 1/2, -13/2 respectively. Find the number of terms in the A.P.​

Answer 1

Answer:

The number of terms (n) in the A.P. is 5⃣9⃣.

Step-by-step explanation:

It is given that,

2nd term of the A.P. =31/4

➡️ a+d = 31/4

➡️ 4a + 4d = 31 ----1⃣

31st term of the A.P. = 1/2

➡️ a + 30d = 1/2

➡️ 2a + 60d = 1 ----2⃣

Now,

Simultaneous equations ➡️ 1⃣ and 2⃣

Multiplying equ. 1⃣ with 2, we get

2(4a + 4d = 31)

and,

Multiplying equ. 2⃣ with 4, we get

4(2a + 60d = 1)

8a + 8d = 62

8a + 240d = 4

- - -

-------------------------------

- 232d = 58

➡ d = 58/(-232)

➡️ d = - 1/4

Therefore, the Common Difference (d) is - 1/4.

From 1⃣, putting d = -1/4, we get

4a + 4( -1/4 ) = 31

➡️ 4a = 31 + 1

➡️ 4a = 32

➡️ a = 8

Therefore, the First Term (a) is 8.

Now,

The last term (l) is given as - 13/2.

We know that,

a + ( n - 1 )d = l

Putting a = 8 and d = - 1/4 , we get

➡️ a + ( n - 1 )d = - 13/2

➡️ 8 + (n - 1)(- 1/4) = - 13/2

➡️ 8 - n/4 + 1/4 = -13/2

➡️ n/4 = 8 + 1/4 + 13/2

➡️ n = 59/4 * 4

➡️ n = 59

Hence, the number of terms in the A.P. is 5⃣9⃣.

❤ HOPE IT HELPS! ❤

REGARDS.

Answer 2

Answer:

the

number

of

terms

are

5

and

9