How to Find the Sum of Given Number of Terms from Indicated Terms ?
By using the formula for an, we may form equations and solve for the variables "a" and "d".
To find the sum of n terms of an arithmetic progression, we may use one of the formulas given below.
Sn = (n/2) [a + l] (or)
Sn = (n/2) [2a + (n - 1)d]
a = first term, d = common difference and n = number of terms.
To find the indicated term, we may use the formula for an.
an = a + (n - 1)d
Question 1 :
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Solution :
n = 22, d = 7
a22 = a + 21d = 149 ----(1)
By applying the value of d in (1), we get
a + 21(7) = 149
a + 147 = 149
a = 149 - 147
a = 2
Now, we have to find sum of 22 terms.
Sn = (n/2) [2a + (n - 1)d]
= (22/2) [2(2) + (22 - 1)7]
= 11 [4 + 21(7)]
= 11 [4 + 147]
= 11 (151)
= 1661
Question 2 :
The sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Solution :
Given that :
Second term (a2) = 14
a + d = 14 -----(1)
Third term (a3) = 18
a + 2d = 18 -----(2)
(1) - (2)
(a + d) - (a + 2d) = 14 - 18
d - 2d = -4
-d = -4
d = 4
By applying the value of d in (1), we will get "a".
a + 4 = 14
a = 14 - 4 = 10
Now, we have to find the sum of 51 terms.
Sn = (n/2) [2a + (n - 1)d]
= (51/2)[2(10) + (51 - 1)4]
= (51/2) [ 20 + 200]
= (51/2)(220)
= 5610
After having gone through the stuff given above, we hope that the students would have understood, how to find the sum of given number of terms from indicated terms.
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