the sum of first 'n' term of an AP is 210 & sum of its first (n-1) term is 171. if the first term 3 , then write the AP
Answers
see the attachment.
Step-by-step explanation:
suppose common difference of AP is d .
Now , sum of first n terms of AP = (n/2){a + (n-1)d}
210 = (n/2){3 + (n-1)d}. .............1
171 = (n-1)/2{ 3 + (n-2)d} ..............2
we just have to solve these equations and after soving we get value of d in terms of n by two different equations . compare both values and then you will get value of n , after that you will get value of d by value of n . and then you will get Ap.
Answer:
Step-by-step explanation:
Given :-
Last term, l = 270 - 171 = 39
First term, a = 3
To Find :-
Arithmetic progression.
Formula to be used :-
S(n) = n/2[a + l]
S(n) = n/2[2a + (n - 1)d]
Solution :-
Putting the given values, we get
S(n) = n/2[a + l]
⇒ 210 = n/2[3 + 39]
⇒ 210 = n/2 × 42
⇒ 420 = 42n
⇒ 420/42 = n
⇒ n = 10
We know A.P. has n terms, so finding common difference, d.
S(n) = n/2[2a + (n - 1)d]
⇒ 210 = 10/2[2 × 3 + (10 - 1)d]
⇒ 210 = 5[6 + 9d]
⇒ 210/5 = 6 + 9d
⇒ 42 = 6 + 9d
⇒ 42 - 6 = 9d
⇒ 36 = 9d
⇒ 36/9 = d
⇒ d = 4
Hence, The Arithmetic progression is 3, 7, 11, 15, ... 39.
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