Question

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Answer 1

QUESTION :- Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of first of its first 20 terms.

ANSWER :-

Given :- A n = $5-6n$

Finding some terms of AP :

Put $n=1$, we get a¹ = -1 [First Term]

Put $n=2$, we get a² = -7 [Second Term]

Common difference (d) = a² - a¹ = $-7-(-1)=-7+1=-6$

Sum of first n terms :-

$Sn = \frac{n}{2} [2a + (n - 1)d]$

$\frac{n}{2} [ - 2 + (n - 1)( - 6)]$

$= n(2 - 3n)$

Sum of first 20 terms :-

$S20 = \frac{20}{2}[2( - 1) + (20 - 1)( - 6)]$

$= 10[( - 2) + 19 \times ( - 6)$

$= 10[ - 2 - 114]$

$= 10[ - 116]$

$\fbox{S20 = - 1160}$

Hence, the sum of its first 20 terms of AP is −1160.

Answer 2

Step-by-step explanation:

see the attachment for answers