Find the sum:(-5) + (-8) + (-11) + . . . + (- 230)

1.	Find the sum:(-5) + (-8) + (-11) + . . . + (- 230)
Answer» We know that the sum of terms for an A.P is given by S_n = \(\frac{n}{2}\)[2a + (n − 1)d] Where; a = first term for the given A.P. d = common difference of the given A.P. n = number of terms Or S_n = \(\frac{n}{2}\)[a + l] Where; a = first term for the given A.P. ;l = last term for the given A.P Given series (-5) + (-8) + (-11) + . . . + (- 230) which is an A.P Where, a = -5 ,d = -8 – (-5) = -3 and last term (a_n= l) = -230 We know that, a_n = a + (n – 1)d So, -230 = -5 + (n – 1)(-3) -230 = -5 – 3n + 3 3n = -2 + 230 n = \(\frac{228}{3}\) = 76 Now, for the sum of these 76 terms S₇₆= \(\frac{76}{2}\) [-5 + (-230)] = 38 x (-235) = -8930 Hence, the sum of terms of the given series is -8930.

Answer»

We know that the sum of terms for an A.P is given by

S_n = \(\frac{n}{2}\)[2a + (n − 1)d]

Where; a = first term for the given A.P. d = common difference of the given A.P. n = number of terms

Or S_n = \(\frac{n}{2}\)[a + l]

Where; a = first term for the given A.P. ;l = last term for the given A.P

Given series (-5) + (-8) + (-11) + . . . + (- 230) which is an A.P

Where, a = -5 ,d = -8 – (-5) = -3 and last term (a_n= l) = -230

We know that, a_n = a + (n – 1)d

So,

-230 = -5 + (n – 1)(-3)

-230 = -5 – 3n + 3

3n = -2 + 230

n = \(\frac{228}{3}\) = 76

Now, for the sum of these 76 terms

S₇₆= \(\frac{76}{2}\) [-5 + (-230)]

= 38 x (-235)

= -8930

Hence, the sum of terms of the given series is -8930.

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