Question

.Find the sum of first 20 terms of AP 2+5+8+......

Answer 1

Answer:

Step-by-step explanation

Answer 2

Given:- $2+5+8+.......$

As we know that sum of n terms in an A.P. is given as-

${S}_{n} = \cfrac{n}{2} \left[ 2a + \left( n - 1 \right) d \right] ..... \left( 1 \right)$

whereas, $a$ and $b$ are the first term and common difference of A.P.

From the given series-

$a=2\\d=5-2 = 3\\n = 20$

Therefore, from equation $\left( 1 \right)$, we have

${S}_{20} = \cfrac{20}{2} \left[ 2 \times 2 + \left( 20 - 1 \right) 3 \right]\\\Rightarrow {S}_{20} = 10 \left( 4 + 57 \right)\\\Rightarrow {S}_{20} = 10 \times 61 = 610$

Hence the sum of $20$ ters of the given series is $610$.