Question

Find the common difference of an ap whose first term is 4

Answer 1

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Answer 2

The complete question is:

Find the common difference of an ap whose first term is 4 and the last term is 49 and the sum of the all its terms is 265

Given:

(i) First term is 4.

(ii) Last term is 49.

(iii) Sum of all terms is 265.

To find:

(i) The common difference in the AP.

Solution:

The formula for the sum of terms in AP is given by:

Sum = (n/2)[a+l]

where a, the first term is 4, Sum is 265 and l, the last term is 49.

So,

(n/2)[4+49] = 265

⇒ (n/2) = 265/53

⇒ (n/2) = 5

⇒ n = 10

There are 10 terms in the AP.

So, the 10th term is the last term and is equal to 49.

nth term in an AP is given as:

an = a + (n-1)d

Taking n as 10, we get,

49 = 4 + 9d

⇒ 9d = 45

⇒ d = 45/9

⇒ d = 5

So, the common difference (d) in the AP is 5.