Question

If 8th and 25th terms of an A.P. are 15 and 49 respectively, then find its first term and common difference.​

Answer 1

Step-by-step explanation:

Given:

• 8th term of A.P is 15 and 25th term of A.P is 49

To Find:

• First term and Common Difference

Solution:

★ We know that nth term of A.P = a+(n–1)d ★

A/q

$\small\implies{\sf }$ a8 = a + 7d = 15 ............(1)

$\small\implies{\sf }$ a25 = a + 24d = 49 ........(2)

† Subtracting equation (1) from (2) †

a + 24d = 49

a + 7d = 15

(-) (-) =(-)

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17d = 34

∴ d = 34/17 = 2

† Put the value of d in equation 1 †

$\small\implies{\sf }$ a + 7d = 15

$\small\implies{\sf }$ a + 7(2) = 15

$\small\implies{\sf }$ a + 14 = 15

$\small\implies{\sf }$ a = 15–14 = 1

Hence, a = 1 & d = 2

Answer 2

$\huge\fcolorbox{red}{pink}{Solution :)}$

Given ,

The 8th term of an AP is 15

It can be written as ,

a + 7d = 15 ----- (i)

and

The 25th term of an AP is 49

It can be written as ,

a + 24d = 49 ----- (ii)

Subtract eq (i) from eq (ii) , we obtain

(a + 24d) - (a + 7d) = 49 - 15

24d - 7d = 34

17d = 34

d = 34/17

d = 2

Put the value of d = 2 in eq (i) , we get

a + 7(2) = 15

a + 14 = 15

a = 15 - 14

a = 1

Hence , the first term and common difference of an AP is 1 and 2

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