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Dear student,
# Answer- a1 + a6 + a11 + a16
# Explaination-
Consider an arithmetic progression with first term a1 and common difference d.
Then nth term is given by
an = a1 + (n-1)d
# Given is,
a1 + a4 + a7 + a10 + a13 + a16 = 147
a1 + a1+3d + a1+6d + a1+9d + a1+12d + a1+15d = 147
6a1 + 45d = 147
2a1 + 15d = 49 ...(1)
# Ti find,
a1 + a6 + a11 + a16 = x
a1 + a1+5d + a1+10d + a1+15d = x
4a1 + 30d = x
2 (2a1 + 15d) = x
2 × 49 = x
x = 98
Hence, a1 + a6 + a11 + a16 = 98.
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