Question

The sum of the series 3 1/2+7+10 1/2+14+....To 17 terms

Answer 1

Answer:

535.5

Step-by-step explanation:

a = 3 1/2 = 7/2

d = 7 - 7/2 = 7/2.

sₙ = n/2(2a + (n-1)d)

s₁₇    = 17/2(2*7/2 + (17-1)7/2)

        = 17/2(7+56) = 17*63/2 = 535.5

Answer 2

Answer:

The sum of the series  3$\frac{1}{2}$+7+10$\frac{1}{2}$+14+..............to 17 terms = 535.5

Step-by-step explanation:

Given series is

3$\frac{1}{2}$+7+10$\frac{1}{2}$+14+..............

To find the sum to 17 terms of this series

Solution:

Given series is  3$\frac{1}{2}$+7+10$\frac{1}{2}$+14+..............

Since 7 -  3$\frac{1}{2}$ =  3$\frac{1}{2}$

10$\frac{1}{2}$ - 7 =  3$\frac{1}{2}$

Since the Third term - second term = Second term -  first term,  the given series is an AP

We have,

The sum to n- terms of an AP, Sₙ = $\frac{n}{2}[2a+(n-1)d]$ --------------(1)

Where 'a' is the first term and 'd' is the common difference of the AP

Here, first term =a= 3$\frac{1}{2}$

Common difference = d = second term - first term = 3$\frac{1}{2}$

n = 17

Then from equation(1), the sum to 17 terms of the AP

$S_{17} = \frac{17}{2} [2X3\frac{1}{2} +16X3\frac{1}{2}]$

= $\frac{17}{2}X2X3\frac{1}{2} [1 +8]$

= $\frac{17}{2}X2X3\frac{1}{2} X9$

= $\frac{1071}{2}$

= 535.5

∴The sum of the series  3$\frac{1}{2}$+7+10$\frac{1}{2}$+14+..............to 17 terms = 535.5

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