Question

In an A.P., the first term is 4 and the last term is 31. If sum of all the terms is 175, find the number of terms and the common difference.

Answer 1

Step 1:

Use the sum formula for an AP: S = `(n/2)(a + l)`

So 175 = `(n/2)(4 + 31) = (n/2)(35).`

Step 2:

175 = `35n/2`    ...[Solve for n]

⇒ 350 = 35n

⇒ n = 10

Step 3: 

Use nth-term formula `a_n = a + (n − 1)d`

To find d:

31 = 4 + (10 − 1)d

⇒ 31 = 4 + 9d

⇒ 9d = 27

⇒ d = 3

Number of terms n = 10; common difference d = 3.