Question

if the sum of the n terms of an AP is 4n-nsquare ,what is the 1st term(that is s1) what is the 2nd term ? similarly find 3rd , 10 th and n^th term​

Answer 1

Answer:

Term1 = 3

T2 = 1

T3= -1

T10 = -15

Step-by-step explanation:

First its stated that , Sn = 4n - nsquare , and term1 (T1) = S1.

So in equation Sn = 4n - nsquare put n=1

S1 = 4×1 - 1square.

=> S1 = 3

Similarily for finding sum of two terms put n=2 in that equation.

S2= 4×2 - 2

=> S2= 4.

Now S2 ( sum of two terms) = T1(first term) + T2(second term)

so here we have the value of S2 and T1 so put them in the above equation to find the value of T2.

S2=T1+T2

=> 4= 3+ T2

=> T2 = 1.

Now form the standard equation of Tn to find any term in the series.

For which we will need the values of - a(first term of the series) , d (common difference in the series).

Here, a=3 , d= -2.

now, Tn = a+(n-1)d

Tn= 3+(n-1)×(-2)

Tn= 5 - 2n.

Now by using this standard form of Tn we can easily derive the value of T3 and T10. Just put the value of n accordingly.

T3 = -1.

T10 = -15.

Hope this will help you.