Question

In an A.P. given that the first term (a) = 54, the common difference
(d) = -3 and the nth term (an) = 0, find n and the sum of first n terms (Sn)
of the A.P.​

Answer 1

Answer:

Step-by-step explanation:

N=19

Sn=513

Answer 2

number of terms  (n) = 19

sum of first n terms = 513

Step-by-step explanation:

here ,

a= 54

d= -3

$a_n=0$

then

$a_n= a+(n-1)d\\0=54+(n-1)-3\\54-3n+3=0\\3n=57\\n = 19$

then sum of first n terms

$S_n = \frac{n}{2}(2a+(n-1)d)\\S_1_9 = \frac{19}{2}(2\times 54+18(-3))\\S_1_9 = \frac{19}{2}(108-54)\\S_1_9 = \frac{19}{2}(54)\\S_1_9 =513$

hence , number of terms  (n) = 19

sum of first n terms = 513

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Given first term of A.P is 5 and common difference is 2. Find 10th term of the A.P​

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