Question

The first and the last term of an A.P. are 4 and 304 respectively and sum of n terms of the A.P. is 15554. Find the number of terms and common difference.​

Answer 1

Step-by-step explanation:

sn = n/2 (a+l)

15554 = n/2 (4+304)

15554 = n/2 *308

15554 = 154n

n = 101

a + (n-1)d = l

4 + (101-1)d = 304

4 + 100d = 304

100d = 304 - 4

100d = 300

d = 300/100

d = 3

no. of terms is 101

common difference is 3

Answer 2

Given:-

• The first and the last term of an Ap are 4 and 304.
• Sum of n term of the Ap is 15554.

To find:-

• Find the common difference and number of terms.

Solutions:-

• Let the number of terms of an Ap be n.

• Sn = n/2 × [a + l]

=> 15554 = n/2 × [4 + 304]

=> 15554 = n/2 × 308

=> 15554 = n × 154

=> 1554/154 = n

=> n = 101

• Let the common difference of an Ap be d.

• l = a + (n - 1)d

=> 304 = 4 + (101 - 1)d

=> 304 = 4 + 100d

=> 304 - 4 = 100d

=> 300 = 100d

=> d = 300/100

=> d = 3

Hence, the number of terms and common difference of Ap are 101 and 3.