Question

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

Answer 1

Hey Mate :
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Here is your answer :
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Given,

8th term = 39

a + 7d = 39 --------(1)

12th term = 59

a + 11d = 59 ---------(2)

Solve 1 & 2

a + 7d = 39
a + 11d = 59
-----------------
-4d = - 20

d = 20/4

d = 5

Substitute d in eq - 1

a + 7d = 39

a + 7 (5) = 39

a + 35 = 39

a = 39 - 35

a = 4


HOPE THIS HELPS U. .

Answer 2

The first term of the AP whose 8th and 12th terms are respectively 39 and 59, is 4.

Given data:

8th and 12th terms of an AP are 39 and 59 respectively

To find:

The first term of the AP

Tips for the solution:

If $t_{1}$ be the first term, $d$ be the common difference, then n–th term is given by

$\boxed{t_{n}=t_{1}+(n-1)d}$

Step-by-step explanation:

Let a be the first term of the AP and d be the common difference.

8th term = 39

➜ a + (8 - 1) d = 39

➜ a + 7d = 39 ... ... (1)

12th term = 59

➜ a + (12 - 1) d = 59

➜ a + 11d = 59 ... ... (2)

Now, (2) - (1) ➜

a + 11d - a - 7d = 59 - 39

➜ 4d = 20

➜ d = 5

Putting d = 5 in (1), we get

a + 7 × 5 = 39

➜ a + 35 = 39

➜ a = 39 - 35

➜ a = 4

Thus the first term of the AP is 4.

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