Question
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
✓
Answer
Given: t17 = 7 + t10 ……(1)
In t17, n = 17
In t10, n = 10
By using nth term of an A.P. formula,
tn = a + (n – 1)d
where n = no. of terms
a = first term
d = common difference
tn = nth term
Thus, on using formula in eq. (1) we get,
⇒ a + (17 – 1)d = 7 + (a + (10 – 1)d)
⇒ a + 16 d = 7 + (a + 9 d)
⇒ a + 16 d – a – 9 d = 7
⇒ 7 d = 7
$\Rightarrow d =\frac{7}{7}=1$
Thus, common difference “d” = 1
In t17, n = 17
In t10, n = 10
By using nth term of an A.P. formula,
tn = a + (n – 1)d
where n = no. of terms
a = first term
d = common difference
tn = nth term
Thus, on using formula in eq. (1) we get,
⇒ a + (17 – 1)d = 7 + (a + (10 – 1)d)
⇒ a + 16 d = 7 + (a + 9 d)
⇒ a + 16 d – a – 9 d = 7
⇒ 7 d = 7
$\Rightarrow d =\frac{7}{7}=1$
Thus, common difference “d” = 1
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