The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.

First term a = 3

Sum of first 20 term = 440

Step-by-step explanation:

Given:

8th term of AP = 17

12th term of AP = 25

Find:

First term a

Sum of first 20 term

Computation:

8th term of AP = 17

a + 7d = 17 EQ1

12th term of AP = 25

a + 11d = 25 EQ2

From EQ1 and EQ2

4d = 8

d = 2

a + 7d = 17

a + 7(2) = 17

First term a = 3

Sum of first 20 term

Sn = [n/2][2a + (n-1)d]

S20 = [20/2][(2)(3) + (20-1)2]

S20 = [10][(6) + 38]

S20 = [10][44]

S20 = 440

Sum of first 20 term = 440

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