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Find the 18th term as well as the sum of the 1st twenty three terms of each of the
following arithmetic sequences:
a) 4; 7; 10; …………….
b) -15; -8; -1; …………

Respuesta :

VirαtKσhli

Step-by-step explanation:

a) 4 , 7 , 10 , . . . . .

Here we can see that ,

  • Common difference = 10-7 = 3
  • First term = 4.

We know the formula of nth term as ,

[tex]\implies T_n = a+(n-1)d\\\\\implies T_{18 }= 4 + (18-1)3 \\\\\implies T_{18} = 4 + 51 \\\\\implies \boxed{ T_{18} = 55 }[/tex]

Sum of 20 terms as ,

[tex]\implies S_n = \dfrac{n}{2}[2a+(n-1)d] \\\\\implies S_{20} = \dfrac{20}{2}[2(4)+(20-1)3] \\\\\implies S_{20} = 10[ 8 + 57 ] \\\\\implies \boxed{ S_{20 }= 650 }[/tex]

b) -15 , -8 , -1 . . . . .

Here we can see that ,

  • Common difference = -8+15 = 7.
  • First term = (-15).

We know the formula of nth term as ,

[tex]\implies T_n = a+(n-1)d\\\\\implies T_{18} = -15 + (18-1)7 \\\\\implies T_{18} = -15+ 119 \\\\\implies \boxed{ T_{18} = 104 }[/tex]

Sum of 20 terms as ,

[tex]\implies S_n = \dfrac{n}{2}[2a+(n-1)d] \\\\\implies S_{20} = \dfrac{20}{2}[2(-15)+(20-1)7] \\\\\implies S_{20} = 10[ -15+ 133 ] \\\\\implies \boxed{ S_{20} = 1180 }[/tex]

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