Question

If a1= 1 and an+1 = 2an+ 5, n = 1, 2 ... , then a100 is equal to

Answer 1

Given:

(i) The first term, a1 = 1

(ii) an+1 = 2an + 5 for n = 1,2,... and so on.

To find:

(i) The value of the 100th term, a100.

Solution:

The sequence on which we are working is an AP.

Given that,

an+1 = 2an + 5

For n=1,

a2 = 2a1 + 5

As we know that, the value of a1 is 1. So, we get,

a2 = 2(1) + 5

= 2+5

=7

Common difference (d) between two consecutive terms = a2 - a1 = 7 - 1

= 6

So, d = 6.

nth term in an AP is given by:

an = a + (n-1)d

For the 100th term, we take n as 100, a as 1 and d as 6.

So,

a100 = 1 + 99(6)

= 1+594

= 595

a100 is equal to 595

Answer 2

Answer:

6 x 2⁹⁹ + 5

Step-by-step explanation:

a1 = 1

a2 = 2a1+ 5 = 2+ 5 = 7

a3 = 14+ 5 = 19

a4 = 38+5 = 43

Seeing options Pattern that satisfies the above numbers is 6 x 2^n - 5

a1 = 1

a2 = 12-5 = 7 a3 = 24-5 = 19

a4 = 48-5 = 43