Question

if the sum of first "n" terms of an arithmetic sequence is 3²n+4n.

a)find the first term and common difference?
b)find the fifth term?
c)first the sum of first five terms?
d)write the nth term of this sequence?​

Answer 1

Answer:

(a) first term = 13 and common difference = 13

(b) fifth term = 65

(c) sum of first five terms = 195

(d) nth term of the sequence = 13n

Step-by-step explanation:

As , Sn = 3^2n + 4n

putting values of n

let n= 1

Sn = 3^2(1) + 4(1) = 13

let n=2

Sn = 3^2(2)+4(2) = 26

let n=3

Sn = 3^2(3)+4(3) = 39

Hence the nbers are = 13 , 26 , 39....

(a) therefore , a= 13 and d= 26-13 = 13

(b). therefore 5th term = t5 = a+4d = 13+4(13) = 65

(c). therefore S5 = 5/2 [ 2(13) + (5-1) 13 ] = 5/2 [ 26+52] = 195

(d) therefore tn = a + (n-1) d = 13 + (n-1) 13 = 13n

THIS IS THE ANSWER