Question

find the sum of the first 23 terms of a AP 7 , 10/2 , 14 . . .

Answer 1

Answer:

1046.5

Step-by-step explanation:

Hi,

Given A.P is 7, 10/2, 14,......

We can clearly observe that

First Term of an A.P , a = 7

Common difference of A.P, d = 10 1/2 - 7 = 21/2 - 7 = 7/2

Sum to n terms of an A.Pis given by

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

To find the sum to 23 terms of an AP,

n = 23

So, S = 23/2[2*7 + (22)7/2]

=> S = 23/2[ 14 + 77]

=> S = 23/2*91

=> S = 2093/2 = 1046.5

Hope, it helped !

Answer 2

given, terms 7 , 10/2 , 14 , ......

first of all, you should find out common difference of given AP.

common difference, d = 10/2 - 7 ≠ 14 - 10/2
seems your question is incorrect..

may be series are 7, 10 1/2 , 14

then, 10 1/2 - 7 = 3.5
14 - 10 1/2 = 3.5

so, common difference , d = 3.5
And first term, a = 7

now, sum of nth term in AP is given by,
$S_n=\frac{n}{2}[2a+(n-1)d]$

so, $S_{23}=\frac{23}{2}[2\times7+(23-1)3.5]$

= 23/2 × (14 + 22 × 3.5)

= 23/2 × (14 + 77)

= 23/2 × 91

= 23 × 91/2

= 1046.5