Question

find the sum of the series 1+5+3+9+5+13+7+17 upto 30 terms​

Answer 1

Answer:

720

Step-by-step explanation:

Given :

Find the sum of the series :

1+5+3+9+5+13+7+17 upto 30 terms​

Solution :

1+5+3+9+5+13+7+17 upto 30 terms​

By keeping odd number terms & even number terms seperately,

We get,

⇒  (1 + 3 + 5 + ... upto 15 terms ) + (5 + 9 + 13 + ... upto 15 terms)

The sum of :

(1 + 3 + 5 + ... upto 15 terms)

We know that,.

The formula for sum upto n terms is :

⇒ $S_n = \frac{n}{2}(2a + (n-1)d)$

here,

a = 1 , d = 2 , n = 15,.

Substituting the given values ,

We get,

⇒ $S_n = \frac{15}{2}(2(1)+(15-1)\times2)$

⇒ $\frac{15}{2}(2+14 \times 2) = \frac{15}{2}(2+28)=\frac{15}{2}(30) = 15 \times 15 = 225$

The sum of :

(5 + 9 + 13 + ... upto 15 terms)

here, a = 5 , d = 4 , n = 15

⇒ $S_n = \frac{n}{2}(2a + (n-1)d)$

⇒ $S_n = \frac{15}{2}(2(5) + (15-1)\times4)$

⇒ $S_n = \frac{15}{2}(2(5) + (14)\times4)$

⇒ $S_n = \frac{15}{2}(10 + (14)\times4)$

⇒ $S_n = \frac{15}{2}(10 + 56)$

⇒ $S_n = \frac{15}{2}(66)$

⇒ $S_n=15 \times 33 = 495$

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∴ 1+5+3+9+5+13+7+17 upto 30 terms​

= (1 + 3 + 5 + ... upto 15 terms ) + (5 + 9 + 13 + ... upto 15 terms)

= 225 + 495 = 720