Question

the 4 th term of an arithmetic sequence is 64 and its 14 th term is 104
a)find the common difference
b)find its 13 th term
c)find the sum of first 25 terms of this sequence
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Answer 1

Step-by-step explanation:

${n}^{th} term \: of \: an \: ap \: is \: = a + (n - 1)d$

$when \: n \: is \: 4 \\ 64 = a + 3d \: \: \: \: \: \: \: \: \: \: \: \: \: eq(1)$

$when \: n \: is \: 14 \\ 104 = a + 13d \: \: \: \: \: \: \: \: \: \: \: \: \: eq(2)$

solving eq 1 and eq 2

$10d = 40 \\ d = 4$

using this in first eqn we can find the first term a

$a = 52$