In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms Solve the word problem
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sum of first 56 terms = 5040
Step-by-step explanation:
19th term is 52
38th term is 128
nth term of an ap = a + (n-1)d
where a is first term & d is common difference
a + 18d = 52 Eq1
a + 37d = 128 Eq2
Eq2 - Eq1
=> 19d = 76
=> d = 4
a + 18*4 = 52
=> a = -20
Sum of n Terms = (n/2)(2a + (n-1)d)
Sum of 56 Terms = (56/2) (2 *(-20) + (55)*4)
= 28 * 180
= 5040
sum of first 56 terms = 5040
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