Question

Find the sum of first 24 terms of the list of numbers whose nth term is given by An=3+2n

Answer 1

Answer:

Step-by-step explanation:

N=1,2,3.....

A1=3+2+1=5

A2=3+2+2=7

A3=3+2+3=9

S24=24/2(2x5+(24-1)2)

=12(10+23x2)

=12(10+46)

=12x56

S24=672

So the answer is 672

I hope this will helps you

Answer 2

Given,

An = 3+2n

To find,

The sum of the first 24 terms.

Solution,

The sum of the first 24 terms will be 672.

We can easily solve this problem by following the given steps.

Now, we know that the sum of AP is found using two formulas.

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

Sn = n/2 [ 2a + (n-1)d]Sn = n/2 (a+l) where n is the last term, a is the first term and d is the common difference between the two terms of an A.P.

According to the question,

An = 3+2n

Now, the first term will be:

A1 = 3 + (2×1)

A1 (a) = 3+2

a = 5

Now, the last term of the A.P. will be:

A24 (l) = 3 + (2×24)

l = 3+48

l = 51

Now, we have a = 5, l = 51 and n = 24. We can easily find the sum of the first 24 terms using the formula, Sn = n/2 (a+l).

Sn = n/2 (a+l)

S24 = 24/2 (5 +51)

S24 = 12 (5+51)

S24 = 12 × 56

S24 = 672

Hence, the sum of the first 24 terms of the A.P. is 672.