Question

find the 31st term of an ap whose 7th term is 34 and 13th term 64​

Answer 1

Answer:

The 31st term of the AP is 154.

Step-by-step explanation:

We are given,

a(7th) = 34

a(13th) = 64

We know that,

a(nth) = a + (n - 1)d

So,

a(7th) = a + (7 - 1)d

34 = a + 6d ----- 1

Similarly,

a(13th) = a + (13 - 1)d

64 = a + 12d ------ 2

Subtracting eq.1 and eq.2 we get,

(a + 12d) - (a + 6d) = 64 - 34

a + 12d - a - 6d = 30

6d = 30

d = 30/6

d = 5

Thus, putting d = 5 in eq.1 we get

34 = a + 6(5)

34 = a + 30

a = 34 - 30

a = 4

Now, we must find the 31st term of this AP

a(31) = 4 + (31 - 1)5

a(31) = 4 + 30(5)

a(31) = 4 + 150

a(31) = 154

Hence, the 31st term of the AP is 154.

Hope it helped and you understood it........All the best