Question

If the nth term of an AP is given by Tn =3n+4,find the common difference of the AP and sum of its first five terms.

Answer 1

nth Term of A. P.

Tn = 3n + 4

Putting the value of n = 1, 2, 3.

For n = 1,

T1 = 3 *1 + 4 = 3 + 4 = 7

For n = 2,

T2 = 3 *2 + 4 = 6 + 4 = 10

For n = 3,

T3 = 3 *3 + 4 = 9 + 4 = 13.

⏺️T2 - T1 = d

10 - 7 = 3

d = 3.

⏺️T3 - T2 = d

13 - 10 = 3.

Since, difference is common.

So, ✔️ Common difference = 3.

♠️AP. = 7, 10, 13.....

SUM OF FIRST FIVE TERMS

=> Sn = n / 2 [ 2a + ( n - 1 ) d ]

=> S5 = 5 / 2 [ 2 *7 + ( 5 - 1 ) 3 ]

=> S5 = 5 / 2 [ 14 + 4*3 ]

=> S5 = 5 / 2 [ 14 + 12 ]

=> S5 = 5 / 2 [ 26]

=> S5 = 5 * 13

=> S5 = 65.

⭕ Sum of first five terms = 65.

Answer 2

answer for the above ques