# Find the first terms and common difference of an A.P. whose t8 = 3 and t12 = 52. - Algebra

Sum

Find the first terms and common difference of an A.P. whose t8 = 3 and t12 = 52.

#### Solution

For an A.P., let a be the first term and d be the common difference.

t8 = 3 and t12 = 52    ......[Given]

Since tn = a + (n – 1)d,

t8 = a + (8 – 1)d

∴ 3 = a + 7d

i.e., a + 7d = 3      ......(i)

Also, t12 = 52

∴ a + (12 – 1)d = 52

∴ a + 11d = 52   ......(ii)

Subtracting equation (i) from (ii), we get

a + 11d = 52
a +   7d = 3
–      –       –
4d = 49

∴ d = 49/4

Substituting d = 49/4 in equation (i), we get

"a" + 7(49/4) = 3

∴ "a" + 343/4 = 3

∴ a = 3 - 343/4

= (-331)/4

∴ The first term and common difference of A.P. are (-331)/4 and 49/4 respectively.

Concept: Arithmetic Progression
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